On the scheme of rare events for a homogeneous Markov chain
type: Item
instance of: scholarly article
title: On the scheme of rare events for a homogeneous Markov chain
zbMATH Open document ID: 0970.60080
DOI: 10.1007/BF02673716
author: V. V. Chichagov
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-11-14T00:00:00Z
review text: The paper is concerned with a discrete-time Markov chain which is stopped as soon as a transition from a specific set of ``rare'' transitions occurs for the \(l\)th time. By letting the probabilities of the rare transitions tend to zero in a suitable way, an asymptotic result is obtained for the vector representing the number of transitions from each state until the chain is stopped. Also, a generalization of this result to semi-Markov processes is presented.
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 1529957
zbMATH Keywords: asymptotic result
zbMATH Keywords: rare event
zbMATH Keywords: sojourn time Markov chain
reviewed by: Erik A. van Doorn
MaRDI profile type: Publication
cites work: Q3969669
cites work: Q4118602
cites work: Limit theorems for Markov random walks with a fixed number of certain transitions
cites work: Q4693044
full work available at URL: https://doi.org/10.1007/bf02673716
OpenAlex ID: W2082666807
description: scientific article; zbMATH DE number 1529957