Asymptotic and spectral properties of exponentially φ-ergodic Markov processes

Details Asymptotic and spectral properties of exponentially φ-ergodic Markov processes Asymptotic and spectral properties of exponentially φ-ergodic Markov processes

2009-11-29

arxiv.org/abs/0911.5473v1

Mathematics

Probability

Scientific paper

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.

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