Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space

Richard L. Tweedie

Stochastic Processes and their Applications, 1975, vol. 3, issue 4, 385-403

Abstract: Let {Xn} be a [empty set][combining character]-irreducible Markov chain on an arbitrary space. Sufficient conditions are given under which the chain is ergodic or recurrent. These extend known results for chains on a countable state space. In particular, it is shown that if the space is a normed topological space, then under some continuity conditions on the transition probabilities of {Xn} the conditions for ergodicity will be met if there is a compact set K and an [epsilon] > 0 such that E {||Xn+1|| -- ||Xn|| | Xn = x} [less-than-or-equals, slant] -[epsilon] whenever x lies outside K and E{||Xn+1|| | Xn=x} is bounded, x [set membership, variant] K; whilst the conditions for recurrence will be met if there exists a compact K with E {||Xn+1|| - ||Xn|| | Xn = x} [less-than-or-equals, slant] 0 for all x outside K. An application to queueing theory is given.

Keywords: recurrence; invariant; measures; positive; recurrence; stationary; measures; ergodicity; waiting; time; Markov; chains; dependent; queues (search for similar items in EconPapers)
Date: 1975
References: Add references at CitEc
Citations: View citations in EconPapers (61)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(75)90033-2
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:3:y:1975:i:4:p:385-403

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().