Volume 17, 2013
|Page(s)||195 - 218|
|Published online||08 February 2013|
Polynomial deviation bounds for recurrent Harris processes having general state space
CNRS UMR 8088, Département de Mathématiques, Université de
2 Département de Mathématiques, Université d’Evry-Val d’Essonne, Bd François Mitterrand, 91025 Evry Cedex, France
Revised: 26 August 2011
Consider a strong Markov process in continuous time, taking values in some Polish state space. Recently, Douc et al. [Stoc. Proc. Appl. 119, (2009) 897–923] introduced verifiable conditions in terms of a supermartingale property implying an explicit control of modulated moments of hitting times. We show how this control can be translated into a control of polynomial moments of abstract regeneration times which are obtained by using the regeneration method of Nummelin, extended to the time-continuous context. As a consequence, if a p-th moment of the regeneration times exists, we obtain non asymptotic deviation bounds of the form Here, f is a bounded function and μ is the invariant measure of the process. We give several examples, including elliptic stochastic differential equations and stochastic differential equations driven by a jump noise.
Mathematics Subject Classification: 60J55 / 60J35 / 60F10 / 62M05
Key words: Harris recurrence / polynomial ergodicity / Nummelin splitting / continuous time Markov processes / drift condition / modulated moment
© EDP Sciences, SMAI, 2013
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