Drift conditions and invariant measures for Markov chains

Authors
Citation
Rl. Tweedie, Drift conditions and invariant measures for Markov chains, STOCH PR AP, 92(2), 2001, pp. 345-354
Citations number
19
Categorie Soggetti
Mathematics
Journal title
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN journal
03044149 → ACNP
Volume
92
Issue
2
Year of publication
2001
Pages
345 - 354
Database
ISI
SICI code
0304-4149(200104)92:2<345:DCAIMF>2.0.ZU;2-L
Abstract
We consider the classical Foster-Lyapunov condition for the existence of an invariant measure for a Markov chain when there are no continuity or irred ucibility assumptions. Provided a weak uniform countable additivity conditi on is satisfied, we show that there are a finite number of orthogonal invar iant measures under the usual drift criterion, and give conditions under wh ich the invariant measure is unique. The structure of these invariant measu res is also identified. These conditions are of particular value for a larg e class of non-linear time series models. (C) 2001 Elsevier Science B.V. Al l rights reserved.