Joint distributions of the numbers of visits for finite-state Markov chains
type: Item
instance of: scholarly article
title: Joint distributions of the numbers of visits for finite-state Markov chains
zbMATH Open document ID: 0938.60062
author: Wolfgang Stadje
published in: Journal of Multivariate Analysis
publication date: 1999-09-22T00:00:00Z
review text: For a discrete-time Markov chain with finite state space \(\{1,\dots, r\}\) we consider the joint distribution of the numbers of visits in states \(1,\dots, r-1\) during the first \(N\) steps or before the \(N\)th visit to \(r\). From the explicit expressions for the corresponding generating functions we obtain the limiting multivariate distributions as \(N\to\infty\) when state \(r\) becomes asymptotically absorbing and for \(J= 1,\dots, r-1\) the probability of a transition from \(r\) to \(j\) is of order \(1/N\).
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1339420
zbMATH Keywords: discrete-time Markov chain
zbMATH Keywords: generating functions
zbMATH Keywords: limiting multivariate distributions
reviewed by: A. D. Barbour
MaRDI profile type: Publication
OpenAlex ID: W2064607448
DOI: 10.1006/JMVA.1999.1814
description: scientific article; zbMATH DE number 1339420