Quasi-stationary Distributions for a Class of Discrete-time Markov Chains

Autor:	Pauline Coolen-Schrijner, Erik A. van Doorn
Rok vydání:	2006
Předmět:	Statistics and Probability Markov chain mixing time Markov chain General Mathematics Discrete phase-type distribution MSC-60J80 Combinatorics Continuous-time Markov chain MSC-60J10 Absorbing Markov chain Balance equation Phase-type distribution Markov property Statistical physics Mathematics
Zdroj:	Methodology and computing in applied probability, 8(4), 449-465. Springer
ISSN:	1573-7713 1387-5841
DOI:	10.1007/s11009-006-0424-y
Popis:	This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution -- actually an infinite family of quasi-stationary distributions -- if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step ({\it killing}) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth-death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dfff02a5f660154539fcf86b8db479c9 https://doi.org/10.1007/s11009-006-0424-y Zobrazit plný text záznamu Plný text ve formátu PDF