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  • Oscillations for order statistics of some discrete processes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Andrea Ottolini

    Suppose k balls are dropped into n boxes independently with uniform probability, where n, k are large with ratio approximately equal to some positive real $\lambda$ . The maximum box count has a counterintuitive behavior: first of all, with high probability it takes at most two values $m_n$ or $m_n+1$ , where $m_n$ is roughly $\frac{\ln n}{\ln \ln n}$ . Moreover, it oscillates between these two values

    更新日期:2020-09-05
  • Perron–Frobenius theory for kernels and Crump–Mode–Jagers processes with macro-individuals
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Serik Sagitov

    Perron–Frobenius theory developed for irreducible non-negative kernels deals with so-called R-positive recurrent kernels. If the kernel M is R-positive recurrent, then the main result determines the limit of the scaled kernel iterations $R^nM^n$ as $n\to\infty$ . 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

    更新日期:2020-09-05
  • On branching models with alarm triggerings
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Claude Lefèvre; Philippe Picard; Sergey Utev

    We discuss a continuous-time Markov branching model in which each individual can trigger an alarm according to a Poisson process. The model is stopped when a given number of alarms is triggered or when there are no more individuals present. Our goal is to determine the distribution of the state of the population at this stopping time. In addition, the state distribution at any fixed time is also obtained

    更新日期:2020-09-05
  • Explicit results on conditional distributions of generalized exponential mixtures
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Claudia Klüppelberg; Miriam Isabel Seifert

    For independent exponentially distributed random variables $X_i$ , $i\in {\mathcal{N}}$ , with distinct rates ${\lambda}_i$ we consider sums $\sum_{i\in\mathcal{A}} X_i$ for $\mathcal{A}\subseteq {\mathcal{N}}$ which follow generalized exponential mixture distributions. We provide novel explicit results on the conditional distribution of the total sum $\sum_{i\in {\mathcal{N}}}X_i$ given that a subset

    更新日期:2020-09-05
  • Existence of Gibbs point processes with stable infinite range interaction
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    David Dereudre; Thibaut Vasseur

    We provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity

    更新日期:2020-09-05
  • Stochastically modeled weakly reversible reaction networks with a single linkage class
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    David F. Anderson; Daniele Cappelletti; Jinsu Kim

    It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so long as the initial condition has strictly positive components). It is conjectured that the stochastically modeled analogs of these systems are positive recurrent

    更新日期:2020-09-05
  • The probabilities of extinction in a branching random walk on a strip
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Peter Braunsteins; Sophie Hautphenne

    We consider a class of multitype Galton–Watson branching processes with a countably infinite type set $\mathcal{X}_d$ whose mean progeny matrices have a block lower Hessenberg form. For these processes, we study the probabilities $\textbf{\textit{q}}(A)$ of extinction in sets of types $A\subseteq \mathcal{X}_d$ . We compare $\textbf{\textit{q}}(A)$ with the global extinction probability $\textbf{\textit{q}}

    更新日期:2020-09-05
  • Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Lu Li; Qinyu Wu; Tiantian Mao

    We investigate stochastic comparisons of parallel systems (corresponding to the largest-order statistics) with respect to the reversed hazard rate and likelihood ratio orders for the proportional reversed hazard rate (PRHR) model. As applications of the main results, we obtain the equivalent characterizations of stochastic comparisons with respect to the reversed hazard rate and likelihood rate orders

    更新日期:2020-09-05
  • Strong convergence of infinite color balanced urns under uniform ergodicity
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Antar Bandyopadhyay; Svante Janson; Debleena Thacker

    We consider the generalization of the Pólya 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 the uniform ergodicity assumption on the associated Markov chain. The proof uses a stochastic coupling of the sequence of chosen colors with a branching Markov chain on a weighted

    更新日期:2020-09-05
  • On some threshold-one attractive interacting particle systems on homogeneous trees
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Y. X. Mu; Y. Zhang

    We consider the threshold-one contact process, the threshold-one voter model and the threshold-one voter model with positive spontaneous death on homogeneous trees $\mathbb{T}_d$ , $d\ge 2$ . Mainly inspired by the corresponding arguments for the contact process, we prove that the complete convergence theorem holds for these three systems under strong survival. When the system survives weakly, complete

    更新日期:2020-09-05
  • On the behavior of the failure rate and reversed failure rate in engineering systems
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Mahdi Tavangar

    In this paper the behaviour of the failure rate and reversed failure rate of an n-component coherent system is studied, where it is assumed that the lifetimes of the components are independent and have a common cumulative distribution function F. Sufficient conditions are provided under which the system failure rate is increasing and the corresponding reversed failure rate is decreasing. We also study

    更新日期:2020-09-05
  • Trees grown under young-age preferential attachment
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Merritt R. Lyon; Hosam M. Mahmoud

    We introduce a class of non-uniform random recursive trees grown with an attachment preference for young age. Via the Chen–Stein method of Poisson approximation, we find that the outdegree of a node is characterized in the limit by ‘perturbed’ Poisson laws, and the perturbation diminishes as the node index increases. As the perturbation is attenuated, a pure Poisson limit ultimately emerges in later

    更新日期:2020-09-05
  • Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Viktor Beneš; Christoph Hofer-Temmel; Günter Last; Jakub Večeřa

    We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation, we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of

    更新日期:2020-09-05
  • Flooding and diameter in general weighted random graphs
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Thomas Mountford; Jacques Saliba

    In this paper we study first passage percolation on a random graph model, the configuration model. We first introduce the notions of weighted diameter, which is the maximum of the weighted lengths of all optimal paths between any two vertices in the graph, and the flooding time, which represents the time (weighted length) needed to reach all the vertices in the graph starting from a uniformly chosen

    更新日期:2020-09-05
  • Randomised rules for stopping problems
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    David Hobson; Matthew Zeng

    In a classical, continuous-time, optimal stopping problem, the agent chooses the best time to stop a stochastic process in order to maximise the expected discounted return. The agent can choose when to stop, and if at any moment they decide to stop, stopping occurs immediately with probability one. However, in many settings this is an idealistic oversimplification. Following Strack and Viefers we consider

    更新日期:2020-09-05
  • On moderate deviations in Poisson approximation
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-09-04
    Qingwei Liu; Aihua Xia

    In this paper we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of a Poisson distribution than those of the normal distribution. We then show that the moderate deviations in Poisson approximation generally require an adjustment and, with suitable adjustment

    更新日期:2020-09-05
  • Representations of component importance for coherent systems with exchangeable components
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    S. Pitzen; M. Burkschat

    Two definitions of Birnbaum’s importance measure for coherent systems are studied in the case of exchangeable components. Representations of these measures in terms of distribution functions of the ordered component lifetimes are given. As an example, coherent systems with failure-dependent component lifetimes based on the notion of sequential order statistics are considered. Furthermore, it is shown

    更新日期:2020-07-16
  • Tertiles and the time constant
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Daniel Ahlberg

    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).

    更新日期:2020-07-16
  • On a class of random walks in simplexes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Tuan-Minh Nguyen; Stanislav Volkov

    We study the limit behaviour of a class of random walk models taking values in the standard d-dimensional ( $d\ge 1$ ) simplex. From an interior point z, the process chooses one of the $d+1$ 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

    更新日期:2020-07-16
  • On the extension of signature-based representations for coherent systems with dependent non-exchangeable components
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Jorge Navarro; Juan Fernández-Sánchez

    The signature representation shows that the reliability of the system is a mixture of the reliability functions of the k-out-of-n systems. The first representation was obtained for systems with independent and identically distributed (IID) components and after it was extended to exchangeable (EXC) components. The purpose of the present paper is to extend it to the class of systems with identically

    更新日期:2020-07-16
  • Asymptotic results on Hoppe trees and their variations
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Ella Hiesmayr; Ümit Işlak

    A uniform recursive tree on n vertices is a random tree where each possible $(n-1)!$ labelled recursive rooted tree is selected with equal probability. We introduce and study weighted trees, a non-uniform recursive tree model departing from the recently introduced Hoppe trees. This class generalizes both uniform recursive trees and Hoppe trees, providing diversity among the nodes and making the model

    更新日期:2020-07-16
  • Randomized near-neighbor graphs, giant components and applications in data science.
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    George C Linderman,Gal Mishne,Ariel Jaffe,Yuval Kluger,Stefan Steinerberger

    If we pick n random points uniformly in $[0,1]^d$ and connect each point to its $c_d \log{n}$ nearest neighbors, where $d\ge 2$ is the dimension and $c_d$ is a constant depending on the dimension, then it is well known that the graph is connected with high probability. We prove that it suffices to connect every point to $ c_{d,1} \log{\log{n}}$ points chosen randomly among its $ c_{d,2} \log{n}$ nearest

    更新日期:2020-07-16
  • Tails of exit times from unstable equilibria on the line
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Yuri Bakhtin; Zsolt Pajor-Gyulai

    For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from Malliavin calculus. In particular, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically

    更新日期:2020-07-16
  • Optimal stopping for measure-valued piecewise deterministic Markov processes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Bertrand Cloez; Benoîte de Saporta; Maud Joubaud

    This paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics of the individuals in a small population. The population and its individual characteristics can be represented by a point measure. We first define a PDMP on a space

    更新日期:2020-07-16
  • Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Hansjörg Albrecher; Bohan Chen; Eleni Vatamidou; Bert Zwart

    We investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin after reinsurance is also regularly varying in terms of the initial capital, and derive an explicit asymptotic expression for the latter. We establish this result

    更新日期:2020-07-16
  • Two results on dynamic extensions of deviation measures
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Mitja Stadje

    We give a dynamic extension result of the (static) notion of a deviation measure. We also study distribution-invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance.

    更新日期:2020-07-16
  • Joint law of an Ornstein–Uhlenbeck process and its supremum
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Christophette Blanchet-Scalliet; Diana Dorobantu; Laura Gay

    Let X be an Ornstein–Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density / distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this

    更新日期:2020-07-16
  • Long-range orientational order of random near-lattice hard sphere and hard disk processes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Alexisz Tamás Gaál

    We show that a point process of hard spheres exhibits long-range orientational order. This process is designed to be a random perturbation of a three-dimensional lattice that satisfies a specific rigidity property; examples include the FCC and HCP lattices. We also define two-dimensional near-lattice processes by local geometry-dependent hard disk conditions. Earlier results about the existence of

    更新日期:2020-07-16
  • Steady-state analysis of load-balancing algorithms in the sub-Halfin–Whitt regime
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Xin Liu; Lei Ying

    We study a class of load-balancing algorithms for many-server systems (N servers). Each server has a buffer of size $b-1$ with $b=O(\sqrt{\log N})$ , i.e. a server can have at most one job in service and $b-1$ jobs queued. We focus on the steady-state performance of load-balancing algorithms in the heavy traffic regime such that the load of the system is $\lambda = 1 - \gamma N^{-\alpha}$ for $0<\alpha<0

    更新日期:2020-07-16
  • Simultaneous ruin probability for two-dimensional brownian risk model
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Krzysztof Dȩbicki; Enkelejd Hashorva; Zbigniew Michna

    The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite time horizon. This is not the case for the simultaneous ruin probability in the two-dimensional Brownian risk model. Relying on asymptotic theory, we derive in this contribution approximations for both simultaneous ruin probability and simultaneous ruin time for the two-dimensional Brownian

    更新日期:2020-07-16
  • Analysis of a spatially inhomogeneous stochastic partial differential equation epidemic model
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Dang H. Nguyen; Nhu N. Nguyen; George Yin

    This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental noise. After setting up the problem, the existence and uniqueness of solutions of the underlying SPDEs are examined. Then, definitions of permanence and extinction are

    更新日期:2020-07-16
  • Central limit theorems for nearly long range dependent subordinated linear processes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Martin Wendler; Wei Biao Wu

    The limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.

    更新日期:2020-07-16
  • On two classes of reflected autoregressive processes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Onno Boxma; Andreas Löpker; Michel Mandjes

    We introduce two general classes of reflected autoregressive processes, INGAR+ and GAR+. Here, INGAR+ can be seen as the counterpart of INAR(1) with general thinning and reflection being imposed to keep the process non-negative; GAR+ relates to AR(1) in an analogous manner. The two processes INGAR+ and GAR+ are shown to be connected via a duality relation. We proceed by presenting a detailed analysis

    更新日期:2020-07-16
  • Limit theory for unbiased and consistent estimators of statistics of random tessellations
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-07-16
    Daniela Flimmel; Zbyněk Pawlas; J. E. Yukich

    We observe a realization of a stationary weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling technique to construct an unbiased estimator of the average value of this geometric characteristic. Under mild conditions on the weights of the cells, we establish variance asymptotics

    更新日期:2020-07-16
  • A renewal theory approach to two-state switching problems with infinite values
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Erik Ekström; Marcus Olofsson; Martin Vannestål

    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

    更新日期:2020-05-04
  • Small-time moderate deviations for the randomised Heston model
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Antoine Jacquier; Fangwei Shi

    We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the Gärtner–Ellis theorem and sharp large deviations tools.

    更新日期:2020-05-04
  • Improvements on the distribution of maximal segmental scores in a Markovian sequence
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    S. Grusea; S. Mercier

    Let $(A_i)_{i \geq 0}$ be a finite-state irreducible aperiodic Markov chain and f a lattice score function such that the average score is negative and positive scores are possible. Define $S_0\coloneqq 0$ and $S_k\coloneqq \sum_{i=1}^k f(A_i)$ the successive partial sums, $S^+$ the maximal non-negative partial sum, $Q_1$ the maximal segmental score of the first excursion above 0, and $M_n\coloneqq

    更新日期:2020-05-04
  • On the occupancy problem for a regime-switching model
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Michael Grabchak; Mark Kelbert; Quentin Paris

    This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed, we assume that they follow a regime-switching Markov chain. For this model, we (1) give finite sample bounds on the expected occupancy probabilities, and (2) provide detailed asymptotics in the case where the underlying

    更新日期:2020-05-04
  • Records for time-dependent stationary Gaussian sequences
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Michael Falk; Amir Khorrami Chokami; Simone A. Padoan

    For a zero-mean, unit-variance stationary univariate Gaussian process we derive the probability that a record at the time n, say $X_n$ , takes place, and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between records. We compute the expected number of records. We also consider two consecutive and non-consecutive

    更新日期:2020-05-04
  • Generalized stacked contact process with variable host fitness
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Eric Foxall; Nicolas Lanchier

    The stacked contact process is a three-state spin system that describes the co-evolution of a population of hosts together with their symbionts. In a nutshell, the hosts evolve according to a contact process while the symbionts evolve according to a contact process on the dynamic subset of the lattice occupied by the host population, indicating that the symbiont can only live within a host. This paper

    更新日期:2020-05-04
  • Directed preferential attachment models: Limiting degree distributions and their tails
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Tom Britton

    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

    更新日期:2020-05-04
  • Integral functionals under the excursion measure
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Maciej Wiśniewolski

    A new approach to the problem of finding the distribution of integral functionals under the excursion measure is presented. It is based on the technique of excursion straddling a time, stochastic analysis, and calculus on local time, and it is done for Brownian motion with drift reflecting at 0, and under some additional assumptions for some class of Itó diffusions. The new method is an alternative

    更新日期:2020-05-04
  • Some new results on stochastic comparisons of coherent systems using signatures
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Ebrahim Amini-Seresht; Baha-Eldin Khaledi; Subhash Kochar

    We consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature

    更新日期:2020-05-04
  • Uniform asymptotic normality of weighted sums of short-memory linear processes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Rimas Norvaiša; Alfredas Račkauskas

    Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q<2$ , let ${\mathcal{F}}$ be a bounded set of real-valued functions on [0, 1] with finite q-variation. It is proved that $\{n^{-1/2}\sum_{i=1}^nX_i\,f(i/n)\colon f\in{\mathcal{F}}\}$ converges in outer distribution in the Banach space of bounded functions on ${\mathcal{F}}$ as $n\to\infty$ . Several applications

    更新日期:2020-05-04
  • A unifying approach to branching processes in a varying environment
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Götz Kersting

    Branching processes $(Z_n)_{n \ge 0}$ in a varying environment generalize the Galton–Watson process, in that they allow time dependence of the offspring distribution. Our main results concern general criteria for almost sure extinction, square integrability of the martingale $(Z_n/\mathrm E[Z_n])_{n \ge 0}$ , properties of the martingale limit W and a Yaglom-type result stating convergence to an exponential

    更新日期:2020-05-04
  • On first passage times of sticky reflecting diffusion processes with double exponential jumps
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Shiyu Song; Yongjin Wang

    We explore the first passage problem for sticky reflecting diffusion processes with double exponential jumps. The joint Laplace transform of the first passage time to an upper level and the corresponding overshoot is studied. In particular, explicit solutions are presented when the diffusion part is driven by a drifted Brownian motion and by an Ornstein–Uhlenbeck process.

    更新日期:2020-05-04
  • Branching processes in a random environment with immigration stopped at zero
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Elena Dyakonova; Doudou Li; Vladimir Vatutin; Mei Zhang

    A critical branching process with immigration which evolves in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the population, we investigate the tail distribution of the so-called life period of the process, i.e. the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment

    更新日期:2020-05-04
  • Weak convergence of random processes with immigration at random times
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Congzao Dong; Alexander Iksanov

    By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. Such random processes generalize random processes with immigration at the epochs of a renewal process which were introduced in Iksanov et al. (2017) and bear a strong resemblance to a random characteristic in general branching

    更新日期:2020-05-04
  • Long-time behavior of Lévy-driven Ornstein–Uhlenbeck processes with regime switching
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Zhongwei Liao; Jinghai Shao

    We investigate the long-time behavior of the Ornstein–Uhlenbeck process driven by Lévy noise with regime switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein–Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Lévy noise and the regime switching described

    更新日期:2020-05-04
  • A functional limit theorem for general shot noise processes
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Alexander Iksanov; Bohdan Rashytov

    By a general shot noise process we mean a shot noise process in which the counting process of shots is arbitrary locally finite. Assuming that the counting process of shots satisfies a functional limit theorem in the Skorokhod space with a locally Hölder continuous Gaussian limit process, and that the response function is regularly varying at infinity, we prove that the corresponding general shot noise

    更新日期:2020-05-04
  • An invariance principle and a large deviation principle for the biased random walk on ${\mathbb{Z}}^{\lowercase{\textbf{\textit{d}}}}$
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Yuelin Liu; Vladas Sidoravicius; Longmin Wang; Kainan Xiang

    We establish an invariance principle and a large deviation principle for a biased random walk ${\text{RW}}_\lambda$ with $\lambda\in [0,1)$ on $\mathbb{Z}^d$ . The scaling limit in the invariance principle is not a d-dimensional Brownian motion. For the large deviation principle, its rate function is different from that of a drifted random walk, as may be expected, though the reflected biased random

    更新日期:2020-05-04
  • Strong convergence of multivariate maxima
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Michael Falk; Simone A. Padoan; Stefano Rizzelli

    It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We extend this result to higher dimensions by considering copulas. We show that the strong convergence result holds for copulas that are in a differential

    更新日期:2020-05-04
  • A model for the spreading of fake news
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Hosam Mahmoud

    We introduce a model for the spreading of fake news in a community of size n. There are $j_n = \alpha n - g_n$ active gullible persons who are willing to believe and spread the fake news, the rest do not react to it. We address the question ‘How long does it take for $r = \rho n - h_n$ persons to become spreaders?’ (The perturbation functions $g_n$ and $h_n$ are o(n), and $0\le \rho \le \alpha\le 1$

    更新日期:2020-05-04
  • A bound on the rate of convergence in the central limit theorem for renewal processes under second moment conditions
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    G. Reinert; C. Yang

    A famous result in renewal theory is the central limit theorem for renewal processes. Since, in applications, usually only observations from a finite time interval are available, a bound on the Kolmogorov distance to the normal distribution is desirable. We provide an explicit non-uniform bound for the renewal central limit theorem based on Stein’s method and track the explicit values of the constants

    更新日期:2020-05-04
  • Optimal stopping for the exponential of a Brownian bridge
    J. Appl. Probab. (IF 0.577) Pub Date : 2020-05-04
    Tiziano de Angelis; Alessandro Milazzo

    We study the problem of stopping a Brownian bridge X in order to maximise the expected value of an exponential gain function. The problem was posed by Ernst and Shepp (2015), and was motivated by bond selling with non-negative prices. Due to the non-linear structure of the exponential gain, we cannot rely on methods used in the literature to find closed-form solutions to other problems involving the

    更新日期:2020-05-04
  • Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration.
    J. Appl. Probab. (IF 0.577) Pub Date : 2017-06-01
    Ollivier Hyrien,Kosto V Mitov,Nikolay M Yanev

    We consider a class of Sevastyanov branching processes with non-homogeneous Poisson immigration. These processes relax the assumption required by the Bellman-Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper, we focus on the subcritical case and examine asymptotic properties

    更新日期:2019-11-01
  • On the estimation of probabilities for birth and death process.
    J. Appl. Probab. (IF 0.577) Pub Date : 1995-09-01
    A I Zeifman

    "Let X(t) be a non-homogeneous birth and death process. In this paper we develop a general method of estimating bounds for the state probabilities for X(t), based on inequalities for the solutions of the forward Kolmogorov equations."

    更新日期:2019-11-01
  • Expected population size in the generation-dependent branching process.
    J. Appl. Probab. (IF 0.577) Pub Date : 1987-06-01
    J D Biggins,T Gotz

    "A Malthusian parameter for the generation-dependent general branching process is introduced and some asymptotics of the expected population size, counted by a general non-negative characteristic, are discussed. Processes both with and without immigration are considered."

    更新日期:2019-11-01
  • A stochastic population projection system based on general age-dependent branching processes.
    J. Appl. Probab. (IF 0.577) Pub Date : 1987-03-01
    C J Mode,M E Jacobson,G T Pickens

    "Algorithms for a stochastic population process, based on assumptions underlying general age-dependent branching processes in discrete time with time inhomogeneous laws of evolution, are developed through the use of a new representation of basic random functions involving birth cohorts and random sums of random variables. New algorithms provide a capability for computing the mean age structure of the

    更新日期:2019-11-01
  • The kin number problem in a multitype Galton-Watson population.
    J. Appl. Probab. (IF 0.577) Pub Date : 1985-03-01
    A Joffe,Waugh Wao

    "The kin number problem in its simplest form is that of the relationship between sibship sizes and offspring numbers.... Further studies have been made, concerning relatives of other degrees of affinity than siblings, but these did not usually yield joint distributions. Recently this aspect of the problem has been studied in the framework of a Galton-Watson process.... In these studies the population

    更新日期:2019-11-01
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