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Asymptotic and spectral properties of exponentially \phi-ergodic Markov processes

Asymptotic and spectral properties of exponentially \phi-ergodic Markov processes,Alexey M. Kulik

Asymptotic and spectral properties of exponentially \phi-ergodic Markov processes
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.
Published in 2009.
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Citations (1)

Exact asymptotic for distribution densities of Levy functionals

Published in 2009.