Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-19T10:28:46.162Z Has data issue: false hasContentIssue false

Correlation decay for Markov maps on a countable state space

Published online by Cambridge University Press:  26 March 2001

VÉRONIQUE MAUME-DESCHAMPS
Affiliation:
Laboratoire de Topologie, Université de Bourgogne – UMR 5584 du CNRS, 9, Avenue Alain Savary, BP 47870, 21078 Dijon Cedex, France (e-mail: vmaume@topolog.u-bourgogne.fr)

Abstract

We estimate the decay of correlations for some Markov maps on a countable state space. A necessary and sufficient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non-quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of finitely many cylinders. Estimates are given for some non-uniformly expanding maps and for maps with bounded jumps.

Type
Research Article
Copyright
© 2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)