Graphes et algorithme de calcul de probabilités stationnaires d'un processus markovien discret. (Graphs and algorithm for the computation of stationary probabilities of a discrete Markov process)
type: Item
instance of: scholarly article
title: Graphes et algorithme de calcul de probabilités stationnaires d'un processus markovien discret. (Graphs and algorithm for the computation of stationary probabilities of a discrete Markov process)
zbMATH Open document ID: 0701.60064
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77368
review text: The author in effect addresses the problem of finding the (unique) stationary distribution \(\{p_ i\}^ n_{i=0}\) corresponding to a finite stochastic matrix \(P=\{p_{ij}\}^ n_{i,j=0}\) satisfying \(p_{ii}=0\) for each i, and containing only one closed set of indices. The approach depends on writing \[ p_ i=Z_ 1'R_ 1'...R'_{k- 1}S_{k,i}R_{k+1}...R_{n-1}Z_{n-1},\quad i\in E_ k,\quad k=0,...,n, \] as an inhomogeneous product of certain non-negative matrices, after decomposing the index set into mutually exclusive subsets \(\{E_ k\}\). The author is, consequently, able to use coefficients of ergodicity [see the reviewer, Non-negative matrices and Markov chains. (1981; Zbl 0471.60001)] as a measure of speed of convergence.
reviewed by: Eugene Seneta
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 4149295
zbMATH Keywords: non-negative matrices
zbMATH Keywords: stationary distribution
zbMATH Keywords: coefficients of ergodicity
zbMATH Keywords: measure of speed of convergence
author: Jean Pellaumail
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4149295