| 1. |
- Ahlberg, Daniel
(författare)
-
Tertiles and the time constant
- 2020
-
Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:2, s. 407-408
-
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).
|
|
| 2. |
- Ajazi, Fioralba, et al.
(författare)
-
Phase transition in random distance graphs on the torus
- 2017
-
Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 54:4, s. 1278-1294
-
Tidskriftsartikel (refereegranskat)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
(författare)
-
CARD COUNTING IN CONTINUOUS TIME
- 2012
-
Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 49:1, s. 184-198
-
Tidskriftsartikel (refereegranskat)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.
(författare)
-
ON EXPECTED DURATIONS OF BIRTH-DEATH PROCESSES, WITH APPLICATIONS TO BRANCHING PROCESSES AND SIS EPIDEMICS
- 2016
-
Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:1, s. 203-215
-
Tidskriftsartikel (refereegranskat)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.
(författare)
-
Strong convergence of infinite color balanced urns under uniform ergodicity
- 2020
-
Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 57:3, s. 853-865
-
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.
|
|
| 6. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
-
On the Time Behaviour of Okazaki Fragments
- 2006
-
Ingår i: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 43, s. 500-509
-
Tidskriftsartikel (refereegranskat)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.
(författare)
-
Phylogenetic confidence intervals for the optimal trait value
- 2015
-
Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 52:4, s. 1115-1132
-
Tidskriftsartikel (refereegranskat)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.
(författare)
-
Disorder detection with costly observations
- 2022
-
Ingår i: Journal of Applied Probability. - : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:2, s. 338-349
-
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.
|
|
| 9. |
|
|
| 10. |
- Belyaev, Yuri K, et al.
(författare)
-
Weakly approaching sequences of random distributions
- 2000
-
Ingår i: Journal of Applied Probability. - Umeå : Umeå universitet. - 0021-9002 .- 1475-6072.
-
Rapport (refereegranskat)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.
|
|
