| 1. |
- Ahlberg, Daniel
(författare)
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Tertiles and the time constant
- 2020
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:2, s. 407-408
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Tidskriftsartikel (refereegranskat)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).
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| 2. |
- Bandyopadhyay, Antar, et al.
(författare)
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Strong convergence of infinite color balanced urns under uniform ergodicity
- 2020
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:3, s. 853-865
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Tidskriftsartikel (refereegranskat)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.
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| 3. |
- Bayraktar, Erhan, et al.
(författare)
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Disorder detection with costly observations
- 2022
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Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:2, s. 338-349
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Tidskriftsartikel (refereegranskat)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.
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| 4. |
- Britton, Tom
(författare)
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Directed preferential attachment models : Limiting degree distributions and their tails
- 2020
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:1, s. 122-136
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Tidskriftsartikel (refereegranskat)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.
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| 5. |
- Comets, Francis, et al.
(författare)
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Generalizations of forest fires with ignition at the origin
- 2023
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 60:2, s. 418-434
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Tidskriftsartikel (refereegranskat)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$ ]]>.
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| 6. |
- Deijfen, Maria, 1975-, et al.
(författare)
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Geometric random intersection graphs with general connection probabilities
- 2024
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Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072.
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Tidskriftsartikel (refereegranskat)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.
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| 7. |
- Ekström, Erik, 1977-, et al.
(författare)
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A renewal theory approach to two-state switching problems with infinite values
- 2020
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Ingår i: Journal of Applied Probability. - : CAMBRIDGE UNIV PRESS. - 0021-9002 .- 1475-6072. ; 57:1, s. 1-18
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Tidskriftsartikel (refereegranskat)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.
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| 8. |
- Ekström, Erik, 1977-, et al.
(författare)
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Monotonicity of implied volatility for perpetual put options
- 2024
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Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 61:1, s. 301-310
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Tidskriftsartikel (refereegranskat)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.
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| 9. |
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| 10. |
- Erhardsson, Torkel, 1966-
(författare)
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Reciprocal properties of random fields on undirected graphs
- 2023
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Ingår i: Journal of Applied Probability. - : CAMBRIDGE UNIV PRESS. - 0021-9002 .- 1475-6072. ; 60:3, s. 781-796
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Tidskriftsartikel (refereegranskat)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.
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| 11. |
- Faouzi, Tarik, et al.
(författare)
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A deep look into the Dagum family of isotropic covariance functions
- 2022
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Ingår i: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:4, s. 1026-1041
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Tidskriftsartikel (refereegranskat)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.
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| 12. |
- Gut, Allan, et al.
(författare)
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Variations of the elephant random walk
- 2021
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Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 58:3, s. 805-829
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Tidskriftsartikel (refereegranskat)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.
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| 13. |
- Janson, Svante, 1955-
(författare)
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Rate of convergence for traditional Polya urns
- 2020
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Ingår i: Journal of Applied Probability. - : CAMBRIDGE UNIV PRESS. - 0021-9002 .- 1475-6072. ; 57:4, s. 1029-1044
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Tidskriftsartikel (refereegranskat)abstract
- Consider a Polya urn with balls of several colours, where balls are drawn sequentially and each drawn ball is immediately replaced together with a fixed number of balls of the same colour. It is well known that the proportions of balls of the different colours converge in distribution to a Dirichlet distribution. We show that the rate of convergence is Theta(1/n) in the minimal L-p metric for any p is an element of [1,infinity], extending a result by Goldstein and Reinert; we further show the same rate for the Levy distance, while the rate for the Kolmogorov distance depends on the parameters, i.e. on the initial composition of the urn. The method used here differs from the one used by Goldstein and Reinert, and uses direct calculations based on the known exact distributions.
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| 14. |
- Nguyen, Tuan Minh, et al.
(författare)
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On a class of random walks in simplexes
- 2020
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:2, s. 409-428
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Tidskriftsartikel (refereegranskat)abstract
- We study the limit behaviour of a class of random walk models taking values in the standard d-dimensional simplex. From an interior point z, the process chooses one of the vertices of the simplex, with probabilities depending on z, and then the particle randomly jumps to a new location z′ on the segment connecting z to the chosen vertex. In some special cases, using properties of the Beta distribution, we prove that the limiting distributions of the Markov chain are Dirichlet. We also consider a related history-dependent random walk model in [0, 1] based on an urn-type scheme. We show that this random walk converges in distribution to an arcsine random variable.
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| 15. |
- Sagitov, Serik, 1956
(författare)
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Critical branching as a pure death process coming down from infinity
- 2023
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 60:2, s. 607-28
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Tidskriftsartikel (refereegranskat)abstract
- We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence of the finite-dimensional distributions, conditioned on non-extinction at a remote time of observation. The limiting process is identified as a pure death process coming down from infinity.This result brings a new perspective on Vatutin's dichotomy, claiming that in the critical regime of age-dependent reproduction, an extant population either contains a large number of short-living individuals or consists of few long-living individuals.
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| 16. |
- Sagitov, Serik, 1956
(författare)
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Perron–Frobenius theory for kernels and Crump–Mode–Jagers processes with macro-individuals
- 2020
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:3, s. 720-733
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Tidskriftsartikel (refereegranskat)abstract
- Perron-Frobenius theory developed for irreducible non-negative kernels deals with socalled R-positive recurrent kernels. If the kernel M is R-positive recurrent, then the main result determines the limit of the scaled kernel iterations (RMn)-M-n as n -> infinity. In Nummelin (1984) this important result is proven using a regeneration method whose major focus is on M having an atom. In the special case when M = P is a stochastic kernel with an atom, the regeneration method has an elegant explanation in terms of an associated split chain. In this paper we give a new probabilistic interpretation of the general regeneration method in terms of multi-type Galton-Watson processes producing clusters of particles. Treating clusters as macro-individuals, we arrive at a single-type Crump-Mode-Jagers process with a naturally embedded renewal structure.
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| 17. |
- Singull, Martin, 1977-, et al.
(författare)
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Large-deviation asymptotics of condition numbers of random matrices
- 2021
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 58:4, s. 1114-1130
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Tidskriftsartikel (refereegranskat)abstract
- Let X be a x random matrix whose entries are independent and identically distributed real random variables with zero mean and unit variance. We study the limiting behaviors of the 2-normal condition number k(p,n) of X in terms of large deviations for large n, with p being fixed or with . We propose two main ingredients: (i) to relate the large-deviation probabilities of k(p,n) to those involving n independent and identically distributed random variables, which enables us to consider a quite general distribution of the entries (namely the sub-Gaussian distribution), and (ii) to control, for standard normal entries, the upper tail of k(p,n) using the upper tails of ratios of two independent random variables, which enables us to establish an application in statistical inference.
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| 18. |
- Uwamariya, Denise, 1985-, et al.
(författare)
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Large deviations of extremal eigenvalues of sample covariance matrices
- 2023
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Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072.
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Tidskriftsartikel (refereegranskat)abstract
- Large deviations of the largest and smallest eigenvalues of XX⊤/n are studied in thisnote, where Xp×n is a p × n random matrix with independent and identically distributed(i.i.d.) sub-Gaussian entries. The assumption imposed on the dimension size p andthe sample size n is p = p(n) → ∞ with p(n) = o(n). This study generalizes one resultobtained in [3].
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