Advances in Applied Probability

Graphical models with heavy-tailed factors can be used to model extremal dependence or causality between extreme events. In a Bayesian network, variables are recursively defined in terms of their parents according to a directed acyclic graph (DAG). We …

The purpose of this study is to present a subgeometric convergence formula for the stationary distribution of the finite-level M/G/1-type Markov chain when taking its infinite-level limit, where the upper boundary level goes to infinity. This study is …

We determine almost sure limits of rescaled intrinsic volumes of the construction steps of fractal percolation in for any dimension . We observe a factorization of these limit variables which allows one, in particular, to determine their expectations …

Inaccuracy and information measures based on cumulative residual entropy are quite useful and have received considerable attention in many fields, such as statistics, probability, and reliability theory. In particular, many authors have studied cumulat…

This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we establish identiti…

Preservation of stochastic orders through the system signature has captured the attention of researchers in recent years. Signature-based comparisons have been made for the usual stochastic order, hazard rate order, and likelihood ratio orders. However…

In 2008, Tóth and Vető defined the self-repelling random walk with directed edges as a non-Markovian random walk on : in this model, the probability that the walk moves from a point of to a given neighbor depends on the number of previous crossings of…

We consider an SIR (susceptible infective recovered) epidemic in a closed population of size n, in which infection spreads via mixing events, comprising individuals chosen uniformly at random from the population, which occur at the points of a Poisso…

We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise deterministic process modeling adaptation is coupled to a Feller logistic diffusion modeling pop…