Generalized multidimensional poisson distributions for finite Markov chains

Tree-valued Markov chains and Poisson-Galton-Watson distributions

The Poisson-Galton-Watson distribution on nite trees, and the related PGW 1 (1) distribution on innnite trees with one end, arise in several contexts, in particular as n ! 1 weak limits within various size-n combinato-rial models. We review this topic, introducingslick notation for describing such distributions. We then describe a family of continuous-time Markov chains whose marginal distribut...

Existence of Stationary Distributions for Finite - State Markov Chains

4.1 The Concept of Stochastic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4.2 Existence of Stationary Distributions for Finite-State Markov Chains . . . . . . . . . 3 4.3 Definitions and Simple Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.4 A Test for Recurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.5 Proving Po...

Lecture 1: Generalized Ray Knight Theorem for Finite Markov Chains

Translated Poisson approximation for Markov chains

The paper is concerned with approximating the distribution of a sum W of integer valued random variables Yi, 1 ≤ i ≤ n, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson distribution, with mean and variance chosen to be close to those of W , and the error is measured with respect to the total variation norm. Error boun...

GENERALIZED CLASS C MARKOV CHAINS AND COMPUTATION OF CLOSED-FORM BOUNDING DISTRIBUTIONS Short title: GENERALIZED CLASS C MARKOV CHAINS

In this paper, we first give a characterization of a class of probability transition matrices having closed-form solutions for transient distributions and the steady-state distribution. We propose to apply stochastic comparison approach to construct bounding chains belonging to this class. Therefore bounding chains can be analyzed efficiently through closed-form solutions in order to provide bo...