Compound Poisson approximation for multiple runs in a Markov chain
type: Item
instance of: scholarly article
title: Compound Poisson approximation for multiple runs in a Markov chain
zbMATH Open document ID: 1018.60079
DOI: 10.1023/A:1022438422611
author: Ourania Chryssaphinou
author: Eutichia Vaggelatou
published in: Annals of the Institute of Statistical Mathematics
publication date: 2003-04-27T00:00:00Z
review text: Let \((X_i)\) be a stationary Markov chain with \(r\)-valued terms. Consider the runs of \(k_i\) \((i = 1,\dots,r)\) consecutive random variables having value \(i\), that end in the finite sequence \(X_1,\dots,X_n\). Then the random variable \(W=\sum^n_{a=1} \sum^r_{i=1} I[(X_{a-k+1},\dots,X_a)=(i,\dots,i)]\) enumerates the overlapping run. Here \(I\) denotes the indicator. The aim of the paper is to estimate the approximation of \(W\)-distribution by compound Poisson; the so called waiting time \(T_k\), i.e. the number of trials until the \(k\)th run appearance \(P(T_k>n)=P(W<k)\), is shown for large \(k\).
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 1901376
zbMATH Keywords: compound Poisson approximation
zbMATH Keywords: consecutive \(k_1,\dots,k_r\) out of \(n\):MFM system
zbMATH Keywords: Kolmogorov distance
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1901376