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Enumeration	Reference	Cover	Find
1.	Ahlberg, Daniel (author) Tertiles and the time constant 2020 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:2, s. 407-408 Journal article (peer-reviewed)abstract We consider planar first-passage percolation and show that the time constant can be bounded by multiples of the first and second tertiles of the weight distribution. As a consequence, we obtain a counter-example to a problem proposed by Alm and Deijfen (2015).
2.	Ajazi, Fioralba, et al. (author) Phase transition in random distance graphs on the torus 2017 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 54:4, s. 1278-1294 Journal article (peer-reviewed)abstract In this paper we consider random distance graphs motivated by applications in neurobiology. These models can be viewed as examples of inhomogeneous random graphs, notably outside of the so-called rank-1 case. Treating these models in the context of the general theory of inhomogeneous graphs helps us to derive the asymptotics for the size of the largest connected component. In particular, we show that certain random distance graphs behave exactly as the classical ErdÅ's-Rényi model, not only in the supercritical phase (as already known) but in the subcritical case as well.
3.	Andersson, Patrik (author) CARD COUNTING IN CONTINUOUS TIME 2012 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 49:1, s. 184-198 Journal article (peer-reviewed)abstract We consider the problem of finding an optimal betting strategy for a house-banked casino card game that is played for several coups before reshuffling. The sampling without replacement makes it possible to take advantage of the changes in the expected value as the deck is depleted, making large bets when the game is advantageous. Using such a strategy, which is easy to implement, is known as card counting. We consider the case of a large number of decks, making an approximation to continuous time possible. A limit law of the return process is found and the optimal card counting strategy is derived. This continuous-time strategy is shown to be a natural analog of the discrete-time strategy where the so-called effects of removal are replaced by the infinitesimal generator of the card process.
4.	Ball, Frank, et al. (author) ON EXPECTED DURATIONS OF BIRTH-DEATH PROCESSES, WITH APPLICATIONS TO BRANCHING PROCESSES AND SIS EPIDEMICS 2016 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:1, s. 203-215 Journal article (peer-reviewed)abstract We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q] = 1, and where the birth rate if the population is currently in state (has size) n is alpha(n). We focus on two important examples, namely alpha(n) = lambda n being a branching process, and alpha(n) = lambda n(N-n)/N which corresponds to an SIS (susceptible -> infective -> susceptible) epidemic model in a homogeneously mixing community of fixed size N. The processes are assumed to start with a single individual, i. e. in state 1. Let T, A(n), C, and S denote the (random) time to extinction, the total time spent in state n, the total number of individuals ever alive, and the sum of the lifetimes of all individuals in the birth-death process, respectively. We give expressions for the expectation of all these quantities and show that these expectations are insensitive to the distribution of Q. We also derive an asymptotic expression for the expected time to extinction of the SIS epidemic, but now starting at the endemic state, which is not independent of the distribution of Q. The results are also applied to the household SIS epidemic, showing that, in contrast to the household SIR (susceptible -> infective -> recovered) epidemic, its threshold parameter R-* is insensitive to the distribution of Q.
5.	Bandyopadhyay, Antar, et al. (author) Strong convergence of infinite color balanced urns under uniform ergodicity 2020 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:3, s. 853-865 Journal article (peer-reviewed)abstract We consider the generalization of the Polya urn scheme with possibly infinitely many colors, as introduced in [37], [4], [5], and [6]. For countably many colors, we prove almost sure convergence of the urn configuration under theuniform ergodicityassumption on the associated Markov chain. The proof uses a stochastic coupling of the sequence of chosen colors with abranching Markov chainon a weightedrandom recursive treeas described in [6], [31], and [26]. Using this coupling we estimate the covariance between any two selected colors. In particular, we re-prove the limit theorem for the classical urn models with finitely many colors.
6.	Bartoszek, Krzysztof, 1984-, et al. (author) On the Time Behaviour of Okazaki Fragments 2006 In: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 43, s. 500-509 Journal article (peer-reviewed)abstract We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.
7.	Bartoszek, Krzysztof, 1984-, et al. (author) Phylogenetic confidence intervals for the optimal trait value 2015 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 52:4, s. 1115-1132 Journal article (peer-reviewed)abstract We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.
8.	Bayraktar, Erhan, et al. (author) Disorder detection with costly observations 2022 In: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:2, s. 338-349 Journal article (peer-reviewed)abstract We study the Wiener disorder detection problem where each observation is associated with a positive cost. In this setting, a strategy is a pair consisting of a sequence of observation times and a stopping time corresponding to the declaration of disorder. We characterize the minimal cost of the disorder problem with costly observations as the unique fixed point of a certain jump operator, and we determine the optimal strategy.
9.	Belyaev, Yuri K, et al. (author) Weakly approaching sequences of random distributions 2000 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 37, s. 807-822 Journal article (peer-reviewed)
10.	Belyaev, Yuri K, et al. (author) Weakly approaching sequences of random distributions 2000 In: Journal of Applied Probability. - Umeå : Umeå universitet. - 0021-9002 .- 1475-6072. Reports (peer-reviewed)abstract We introduce the notion of weakly approaching sequences of distributions, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.
11.	Björnberg, Jakob E., et al. (author) A Stochastic Model for Virus Growth in a Cell Population 2014 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 51:3, s. 599-612 Journal article (peer-reviewed)abstract In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter A which quantifies the 'aggressiveness' of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to lambda = 0. This is in agreement with experimental data about real viruses.
12.	Björnberg, Jakob E., et al. (author) Coexistence and noncoexistence of Markovian viruses and their hosts 2014 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 51:1, s. 191-208 Journal article (peer-reviewed)abstract Examining possibilities for the coexistence of two competing populations is a classic problem which dates back to the earliest 'predator-prey' models. In this paper we study this problem in the context of a model introduced in Bjornberg et al. (2012) for the spread of a virus infection in a population of healthy cells. The infected cells may be seen as a population of 'predators' and the healthy cells as a population of 'prey'. We show that, depending on the parameters defining the model, there may or may not be coexistence of the two populations, and we give precise criteria for this.
13.	Britton, Tom, et al. (author) A dynamic network in a dynamic population: asymptotic properties 2011 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 1475-6072 .- 0021-9002. ; 48:4, s. 1163-1178 Journal article (peer-reviewed)abstract We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters.
14.	Britton, Tom (author) Directed preferential attachment models : Limiting degree distributions and their tails 2020 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:1, s. 122-136 Journal article (peer-reviewed)abstract The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two independent pure birth processes that are observed at a common exponentially distributed time T (thus creating dependence between in- and out-degree). The characterization gives an explicit form for the joint degree distribution, and this confirms previously derived tail probabilities for the two marginal degree distributions. The new characterization is also used to obtain an explicit expression for tail probabilities in which both degrees are large. A new generalized directed preferential attachment model is then defined and analyzed using similar methods. The two extensions, motivated by empirical evidence, are to allow double-directed (i.e. undirected) edges in the network, and to allow the probability of connecting an ingoing (outgoing) edge to a specified node to also depend on the out-degree (in-degree) of that node.
15.	Britton, Tom, et al. (author) Epidemics on random graphs with tunable clustering 2008 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 45:3, s. 743-756 Journal article (peer-reviewed)abstract In this paper a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large outbreak in the epidemic. We investigate how these quantities vary with the clustering in the graph and find that, as the clustering increases, the epidemic threshold decreases. The network is modeled by a random intersection graph, in which individuals are independently members of a number of groups and two individuals are linked to each other if and only if there is at least one group that they are both members of.
16.	Britton, Tom, et al. (author) Maximizing the size of the giant 2012 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 49:4, s. 1156-1165 Journal article (peer-reviewed)abstract Consider a random graph where the mean degree is given and fixed. In this paper we derive the maximal size of the largest connected component in the graph. We also study the related question of the largest possible outbreak size of an epidemic occurring 'on' the random graph (the graph describing the social structure in the community). More precisely, we look at two different classes of random graphs. First, the Poissonian random graph in which each node i is given an independent and identically distributed (i.i.d.) random weight X-i with E(X-i) = mu, and where there is an edge between i and j with probability 1 - e(-XiXj/(mu n)), independently of other edges. The second model is the thinned configuration model in which then vertices of the ground graph have i.i.d. ground degrees, distributed as D, with E(D) = mu. The graph of interest is obtained by deleting edges independently with probability 1 - p. In both models the fraction of vertices in the largest connected component converges in probability to a constant 1 - q, where q depends on X or D and p. We investigate for which distributions X and D with given mu and p, 1 - q is maximized. We show that in the class of Poissonian random graphs, X should have all its mass at 0 and one other real, which can be explicitly determined. For the thinned configuration model, D should have all its mass at 0 and two subsequent positive integers.
17.	Britton, Tom, et al. (author) The early stage behaviour of a stochastic SIR epidemic with term-time forcing 2009 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 46:4, s. 975-992 Journal article (peer-reviewed)abstract The general stochastic SIR epidemic in a closed population under the influence of a term-time forced environment is considered. An 'environment' in this context is any external factor that influences the contact rate between individuals in the population, but is itself unaffected by the population. Here 'term-time forcing' refers to discontinuous but cyclic changes in the contact rate. The inclusion of such an environment into the model is done by replacing a single contact rate λ with a cyclically alternating renewal process with k different states denoted {A(t)}t≥0. Threshold conditions in terms of R⋆ are obtained, such that R⋆ > 1 implies that π, the probability of a large outbreak, is strictly positive. Examples are given where π is evaluated numerically from which the impact of the distribution of the time periods that Λ(t) spends in its different states is clearly seen.
18.	Budhiraja, Amarjit, et al. (author) Large deviations for multidimensional state-dependent shot noise processes 2015 In: Journal of Applied Probability. - : Applied Probability Trust. - 0021-9002 .- 1475-6072. ; 52:4, s. 1097-1114 Journal article (peer-reviewed)abstract Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.
19.	Christensen, Sören, 1982 (author) Phase-type distributions and optimal stopping for autoregressive processes 2012 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 49:1, s. 22-39 Journal article (peer-reviewed)abstract Autoregressive processes are intensively studied in statistics and other fields of applied stochastics. For many applications, the overshoot and the threshold time are of special interest. When the upward innovations are in the class of phase-type distributions, we determine the joint distribution of these two quantities and apply this result to problems of optimal stopping. Using a principle of continuous fit, this leads to explicit solutions. © 2012 Applied Probability Trust.
20.	Comets, Francis, et al. (author) Generalizations of forest fires with ignition at the origin 2023 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 60:2, s. 418-434 Journal article (peer-reviewed)abstract We study generalizations of the forest fire model introduced in [4] and [10] by allowing the rates at which the trees grow to depend on their location, introducing long-range burning, as well as a continuous-space generalization of the model. We establish that in all the models in consideration the expected time required to reach a site at distance x from the origin is of order for any 0$ ]]>.
21.	Deijfen, Maria, 1975-, et al. (author) Geometric random intersection graphs with general connection probabilities 2024 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. Journal article (peer-reviewed)abstract Let $\mathcal{V}$ and $\mathcal{U}$ be the point sets of two independent homogeneous Poisson processes on $\mathbb{R}<^>d$ . A graph $\mathcal{G}_\mathcal{V}$ with vertex set $\mathcal{V}$ is constructed by first connecting pairs of points (v, u) with $v\in\mathcal{V}$ and $u\in\mathcal{U}$ independently with probability $g(v-u)$ , where g is a non-increasing radial function, and then connecting two points $v_1,v_2\in\mathcal{V}$ if and only if they have a joint neighbor $u\in\mathcal{U}$ . This gives rise to a random intersection graph on $\mathbb{R}<^>d$ . Local properties of the graph, including the degree distribution, are investigated and quantified in terms of the intensities of the underlying Poisson processes and the function g. Furthermore, the percolation properties of the graph are characterized and shown to differ depending on whether g has bounded or unbounded support.
22.	Deijfen, Maria, 1975- (author) Random networks with preferential growth and vertex death 2010 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 47:4, s. 1150-1163 Journal article (peer-reviewed)abstract A dynamic model for a random network evolving in continuous time is defined, where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is connected to an existing vertex with probability proportional to a function b of the fitness of the existing vertex. Furthermore, a vertex dies at a rate given by a function d of its fitness. Using results from the theory of general branching processes, an expression for the asymptotic empirical fitness distribution {pk} is derived and analyzed for a number of specific choices of b and d. When b(i) = i + α and d(i) = β, that is, linear preferential attachment for the newborn and random deaths, then pk ∼ k-(2+α). When b(i) = i + 1 and d(i) = β(i + 1), with β < 1, then pk ∼ (1 + β)-k, that is, if the death rate is also proportional to the fitness, then the power-law distribution is lost. Furthermore, when b(i) = i + 1 and d(i) = β(i + 1)γ, with β, γ < 1, then logpk ∼ -kγ, a stretched exponential distribution. The momentaneous in-degrees are also studied and simulations suggest that their behaviour is qualitatively similar to that of the fitnesses.
23.	Deijfen, Maria, et al. (author) Routeing on trees 2016 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:2, s. 475-488 Journal article (peer-reviewed)abstract We consider three different schemes for signal routeing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with independent and identically distributed weights representing the strength of the transceivers. The edges of the tree are also equipped with independent and identically distributed weights, representing the costs for passing the edges. For each one of our schemes, we derive sharp conditions on the distributions of the vertex weights and the edge weights that determine when the root can transmit a signal over arbitrarily large distances.
24.	Ekström, Erik, 1977-, et al. (author) A renewal theory approach to two-state switching problems with infinite values 2020 In: Journal of Applied Probability. - : CAMBRIDGE UNIV PRESS. - 0021-9002 .- 1475-6072. ; 57:1, s. 1-18 Journal article (peer-reviewed)abstract We study a renewal theory approach to perpetual two-state switching problems with infinite value functions. Since the corresponding value functions are infinite, the problems fall outside the standard class of problems which can be analyzed using dynamic programming. Instead, we propose an alternative formulation of optimal switching theory in which optimality of a strategy is defined in terms of its long-term mean return, which can be determined using renewal theory. The approach is illustrated by examples in connection with trend-following strategies in finance.
25.	Ekström, Erik, 1977- (author) Bounds for perpetual American option prices in a jump-diffusion model 2006 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 43:3, s. 867-873 Journal article (peer-reviewed)abstract We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black–Scholes model. We also investigate the dependence of the bounds on different parameters of the model.
26.	Ekström, Erik, 1977-, et al. (author) Dynkin Games With Heterogeneous Beliefs 2017 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 54:1, s. 236-251 Journal article (peer-reviewed)abstract We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions, then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.
27.	Ekström, Erik, et al. (author) Momentum liquidation under partial information 2016 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:2, s. 341-359 Journal article (peer-reviewed)abstract Momentum is the notion that an asset that has performed well in the past will continue to do so for some period. We study the optimal liquidation strategy for a momentum trade in a setting where the drift of the asset drops from a high value to a smaller one at some random change-point. This change-point is not directly observable for the trader, but it is partially observable in the sense that it coincides with one of the jump times of some exogenous Poisson process representing external shocks, and these jump times are assumed to be observable. Comparisons with existing results for momentum trading under incomplete information show that the assumption that the disappearance of the momentum effect is triggered by observable external shocks significantly improves the optimal strategy.
28.	Ekström, Erik, 1977-, et al. (author) Monotonicity of implied volatility for perpetual put options 2024 In: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 61:1, s. 301-310 Journal article (peer-reviewed)abstract We define and study properties of implied volatility for American perpetual put options. In particular, we show that if the market prices are derived from a local volatility model with a monotone volatility function, then the corresponding implied volatility is also monotone as a function of the strike price.
29.	Ekström, Erik, et al. (author) Optimal closing of a momentum trade 2013 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 50:2, s. 374-387 Journal article (peer-reviewed)abstract There is an extensive academic literature that documents that stocks which have performed well in the past often continue to perform well over some holding period-so-called momentum. We study the optimal timing for an asset sale for an agent with a long position in a momentum trade. The asset price is modelled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time. The problem of optimal selling of the asset is then formulated as an optimal stopping problem under incomplete information. Based on the observations of the asset, the agent wants to detect the unobservable change point as accurately as possible. Using filtering techniques and stochastic analysis, we reduce the problem to a one-dimensional optimal stopping problem, which we solve explicitly. We also show that the optimal boundary at which the investor should liquidate the trade depends monotonically on the model parameters.
30.	Ekström, Erik, et al. (author) Optimal liquidation of a call spread 2010 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 47:2, s. 586-593 Journal article (peer-reviewed)abstract We study the optimal liquidation strategy for a call spread in the case when an investor, who does not hedge, believes in a volatility that differs from the implied volatility. The liquidation problem is formulated as an optimal stopping problem, which we solve explicitly. We also provide a sensitivity analysis with respect to the model parameters.
31.	Ekström, Erik, et al. (author) Optimal stopping of a Brownian bridge 2009 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 46:1, s. 170-180 Journal article (peer-reviewed)abstract We study several optimal stopping problems in which the gains process is a Brownian bridge or a functional of a Brownian bridge. Our examples constitute natural finite-horizon optimal stopping problems with explicit solutions.
32.	Ekström, Erik, 1977-, et al. (author) Stopping problems with an unknown state 2023 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. Journal article (peer-reviewed)
33.	Ekström, Erik, et al. (author) Superreplication of options on several underlying assets 2005 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 42:1, s. 27-38 Journal article (peer-reviewed)
34.	Erhardsson, Torkel, 1966- (author) Reciprocal properties of random fields on undirected graphs 2023 In: Journal of Applied Probability. - : CAMBRIDGE UNIV PRESS. - 0021-9002 .- 1475-6072. ; 60:3, s. 781-796 Journal article (peer-reviewed)abstract We clarify and refine the definition of a reciprocal random field on an undirected graph, with the reciprocal chain as a special case, by introducing four new properties: the factorizing, global, local, and pairwise reciprocal properties, in decreasing order of strength, with respect to a set of nodes delta. They reduce to the better-known Markov properties if 8 is the empty set, or, with the exception of the local property, if delta is a complete set. Conditions for each reciprocal property to imply the next stronger property are derived, and it is shown that, conditionally on the values at a set of nodes delta(0), all four properties are preserved for the subgraph induced by the remaining nodes, with respect to the node set delta \ delta(0). We note that many of the above results are new even for reciprocal chains.
35.	Faouzi, Tarik, et al. (author) A deep look into the Dagum family of isotropic covariance functions 2022 In: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:4, s. 1026-1041 Journal article (peer-reviewed)abstract The Dagum family of isotropic covariance functions has two parameters that allow fordecoupling of the fractal dimension and the Hurst effect for Gaussian random fields thatare stationary and isotropic over Euclidean spaces. Sufficient conditions that allow forpositive definiteness in $R^d$ of the Dagum family have been proposed on the basis ofthe fact that the Dagum family allows for complete monotonicity under some parameter restrictions. The spectral properties of the Dagum family have been inspected to a verylimited extent only, and this paper gives insight into this direction. Specifically, we studyfinite and asymptotic properties of the isotropic spectral density (intended as the Hankeltransform) of the Dagum model. Also, we establish some closed-form expressions forthe Dagum spectral density in terms of the Fox–Wright functions. Finally, we provideasymptotic properties for such a class of spectral densities.
36.	Gabrysch, Katja (author) Convergence of directed random graphs to the Poisson-weighted infinite tree 2016 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:2, s. 463-474 Journal article (peer-reviewed)abstract We consider a directed graph on the integers with a directed edge from vertex i to j present with probability n-1, whenever i-1(j - i). We show that the closure of vertex 0 in such a weighted random graph converges in distribution to the Poisson-weighted infinite tree as n→∞. In addition, we derive limit theorems for the length of the longest path in the subgraph of the Poisson-weighted infinite tree which has all vertices at weighted distance of at most ρ from the root.
37.	Gabrysch, Katja (author) Distribution of the smallest visited point in a greedy walk on the line 2016 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:3, s. 880-887 Journal article (peer-reviewed)abstract We consider a greedy walk on a Poisson process on the real line. It is known that the walk does not visit all points of the process. In this paper we first obtain some useful independence properties associated with this process which enable us to compute the distribution of the sequence of indices of visited points. Given that the walk tends to +∞, we find the distribution of the number of visited points in the negative half-line, as well as the distribution of the time at which the walk achieves its minimum.
38.	Grandell, Jan, et al. (author) Ruin probabilities in a diffusion environment 2011 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 48A, s. 39-50 Journal article (peer-reviewed)abstract We consider an insurance model, where the underlying point process is a Cox process. Using a martingale approach applied to diffusion processes, finite-time Lundberg inequalities are obtained. By change-of-measure techniques, Cramer-Lundberg approximations are derived.
39.	Gudmundsson, Thorbjörn, et al. (author) Markov chain monte carlo for computing rare-event probabilities for a heavy-tailed random walk 2014 In: Journal of Applied Probability. - : Applied Probability Trust. - 0021-9002 .- 1475-6072. ; 51:2, s. 359-376 Journal article (peer-reviewed)abstract In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability of the rare event as its normalizing constant. Using the MCMC methodology, a Markov chain is simulated, with the aforementioned conditional distribution as its invariant distribution, and information about the normalizing constant is extracted from its trajectory. The algorithm is described in full generality and applied to the problem of computing the probability that a heavy-tailed random walk exceeds a high threshold. An unbiased estimator of the reciprocal probability is constructed whose normalized variance vanishes asymptotically. The algorithm is extended to random sums and its performance is illustrated numerically and compared to existing importance sampling algorithms.
40.	Gut, Allan (author) Limit theorems for a generalized St Petersburg game 2010 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 47:3, s. 752-760 Journal article (peer-reviewed)abstract The topic of the present paper is a generalized St Petersburg game in which the distribution of the payoff X is given by P(X = sr((k-1)/alpha)) = pq(k-1), k = 1,2, ..., where p + q = 1, s = l/p, r = 1/q, and 0 < alpha <= 1. For the case in which alpha = 1, we extend Feller's classical weak law and Martin-Lof's theorem on convergence in distribution along the 2"-subsequence. The analog for 0 < alpha < 1 turns out to converge in distribution to an asymmetric stable law with index a. Finally, some limit theorems for polynomial and geometric size total gains, as well as for extremes, are given.
41.	Gut, Allan, et al. (author) Variations of the elephant random walk 2021 In: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 58:3, s. 805-829 Journal article (peer-reviewed)abstract In the classical simple random walk the steps are independent, that is, the walker has no memory. In contrast, in the elephant random walk, which was introduced by Schutz and Trimper [19] in 2004, the next step always depends on the whole path so far. Our main aim is to prove analogous results when the elephant has only a restricted memory, for example remembering only the most remote step(s), the most recent step(s), or both. We also extend the models to cover more general step sizes.
42.	Gyllenberg, Mats, et al. (author) Non-uniqueness in probabilistic numerical identification of bacteria 1994 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 31:2, s. 542-548 Journal article (peer-reviewed)abstract In this note we point out an inherent difficulty in numerical identification of bacteria. The problem is that of uniqueness of the taxonomic structure or, in mathematical terms, the lack of statistical identifiability of finite mixtures of multivariate Bernoulli probability distributions shown here.
43.	Hammarlid, Ola (author) Tools to estimate the first passage time to a convex barrier 2005 In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 42:1, s. 61-81 Journal article (peer-reviewed)abstract he first passage time of a random walk to a barrier (constant or concave) is of great importance in many areas, such as insurance, finance, and sequential analysis. Here, we consider a sum of independent, identically distributed random variables and the convex barrier cb(n/c), where c is a scale parameter and n is time. It is shown, using large-deviation techniques, that the limit distribution of the first passage time decays exponentially in c. Under a tilt of measure, which changes the drift, four properties are proved: the limit distribution of the overshoot is distributed as an overshoot over a linear barrier; the stopping time is asymptotically normally distributed when it is properly normalized; the overshoot and the asymptotic normal part are asymptotically independent; and the overshoot over a linear bather is bounded by an exponentially distributed random variable. The determination of the function that multiplies the exponential part is guided by consideration of these properties.
44.	Holst, Lars (author) A NOTE ON EMBEDDING CERTAIN BERNOULLI SEQUENCES IN MARKED POISSON PROCESSES 2008 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 45:4, s. 1181-1185 Journal article (peer-reviewed)abstract A sequence of independent Bernoulli random variables with success probabilities a/(a + b + k - 1), k = 1, 2, 3, ... , is embedded in a marked Poisson process with intensity 1. Using this, conditional Poisson limits follow for counts of failure strings.
45.	Holst, Lars (author) Counts of failure strings in certain Bernoulli sequences 2007 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 44:3, s. 824-830 Journal article (peer-reviewed)abstract In a sequence of independent Bernoulli trials the probability for success in the kth trial is Pk k = 1, 2..... The number of strings with a given number of failures between two subsequent successes is studied. Explicit expressions for distributions and moments are obtained for the case in which Pk = a/(a + b + k - 1), a > 0, b >= 0. Also, the limit behaviour of the longest failure string in the first n trials is considered. For b = 0, the strings correspond to cycles in random permutations.
46.	Holst, Lars (author) ON CONSECUTIVE RECORDS IN CERTAIN BERNOULLI SEQUENCES 2009 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 46:4, s. 1201-1208 Journal article (peer-reviewed)abstract In an infinite sequence of independent Bernoulli trials with success probabilities p(k) = a/(a + b + k - 1) for k = 1, 2 3, ... , let N-r be the number of r >= 2 consecutive successes. Expressions for the first two moments of N-r are derived. Asymptotics of the probability of no occurrence of r consecutive successes for large r are obtained. Using an embedding in a marked Poisson process, it is indicated how the distribution of N-r can be calculated for small r.
47.	Holst, Lars (author) Probabilistic proofs of euler identities 2013 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 50:4, s. 1206-1212 Journal article (peer-reviewed)abstract Formulae for zeta(2n) and L-chi 4 (2n + 1) involving Euler and tangent numbers are derived using the hyperbolic secant probability distribution and its moment generating function. In particular, the Basel problem, where zeta(2) = pi(2)/6, is considered. Euler's infinite product for the sine is also proved using the distribution of sums of independent hyperbolic secant random variables and a local limit theorem.
48.	Holst, Lars, et al. (author) RUNS IN COIN TOSSING : A GENERAL APPROACH FOR DERIVING DISTRIBUTIONS FOR FUNCTIONALS 2015 In: Journal of Applied Probability. - : APPLIED PROBABILITY TRUST. - 0021-9002 .- 1475-6072. ; 52:3, s. 752-770 Journal article (peer-reviewed)abstract We take a fresh look at the classical problem of runs in a sequence of independent and identically distributed coin tosses and derive a general identity/recursion which can be used to compute (joint) distributions of functionals of run types. This generalizes and unifies already existing approaches. We give several examples, derive asymptotics, and pose some further questions.
49.	Holst, Lars (author) The number of two consecutive successes in a Hoppe-Pólya urn 2008 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 45:3, s. 901-906 Journal article (peer-reviewed)abstract In a sequence of independent Bernoulli trials the probability of success in the kth trial is pk = a/(a + b + k - 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.
50.	Hult, Henrik, et al. (author) Large deviations for point processes based on stationary sequences with heavy tails 2010 In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 47:1, s. 1-40 Journal article (peer-reviewed)abstract In this paper we propose a framework that facilitates the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track both of the magnitude of the extreme values of a process and the order in which these extreme values appear. Particular emphasis is put on (infinite) linear processes with random coefficients. The proposed framework provides a fairly complete description of the joint asymptotic behavior of the large values of the stationary sequence. We apply the general result on large deviations for point processes to derive the asymptotic decay of certain probabilities related to partial sum processes as well as ruin probabilities.

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