Asymptotic and spectral properties of exponentially \phi-ergodic Markov processes
Abstract
New relations between ergodic rate, L_p convergence rates, and asymptotic behavior of tail probabilities for hitting times of a time homogeneous Markov process are established. For L_p convergence rates and related spectral and functional properties (spectral gap and Poincare inequality) sufficient conditions are given in the terms of an exponential \phi-coupling. This provides sufficient conditions for L_p convergence rates in the terms of appropriate combination of `local mixing' and `recurrence' conditions on the initial process, typical in the ergodic theory of Markov processes. The range of application of the approach includes time-irreversible processes. In particular, sufficient conditions for spectral gap property for Levy driven Ornstein-Uhlenbeck process are established.
Keywords
Cite
@article{arxiv.0911.5473,
title = {Asymptotic and spectral properties of exponentially \phi-ergodic Markov processes},
author = {Alexey M. Kulik},
journal= {arXiv preprint arXiv:0911.5473},
year = {2009}
}