Related papers: Finite / Countable State Space Stochastic Processe…

We study certain properties of the function space of autocorrelation functions of Unit Continuous Time Markov Chains (CTMCs). It is shown that under particular conditions, the $L^p$ norm of the autocorrelation function of arbitrary finite…

Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…

We study the synchronization behavior of discrete-time Markov chains on countable state spaces. Representing a Markov chain in terms of a random dynamical system, which describes the collective dynamics of trajectories driven by the same…

This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length…

We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional…

We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…

The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…

We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

This document presents a compilation of results related to the theory of stochastic processes, with a specific focus on Markov processes, regenerative processes, renewal processes, and stationary processes. The relevance of these topics…

It is shown that large deviation statistical quantities of the discrete time, finite state Markov process $P_{n+1}^{(j)}=\sum_{k=1}^NH_{jk}P_n^{(k)}$, where P_n^{(j)} is the probability for the j-state at the time step n and H_{jk} is the…

U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…

Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with…

The aim of this paper is threefold. Firstly, we develop the author's previous work on the dynamical relationship between determinantal point processes and CAR algebras. Secondly, we present a novel application of the theory of stochastic…

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…

In the paper we study continuous time controlled Markov processes using discrete time controlled Markov processes. We consider long run functionals: average reward per unit time or long run risk sensitive functional. We also investigate…

We discuss the relationship between discrete-time processes (chains) and one-dimensional Gibbs measures. We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic…

We consider the almost semi-continuous processes defined on a finite Markov chain. The representation of the moment generating functions for the absolute maximum after achievement positive level and for the recovery time are obtained.…

We consider two important time scales---the Markov and cryptic orders---that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated…