Issue |
ESAIM: PS
Volume 17, 2013
|
|
---|---|---|
Page(s) | 195 - 218 | |
DOI | https://doi.org/10.1051/ps/2011156 | |
Published online | 08 February 2013 |
Polynomial deviation bounds for recurrent Harris processes having general state space
1
CNRS UMR 8088, Département de Mathématiques, Université de
Cergy-Pontoise, 95000
Cergy-Pontoise,
France
eva.loecherbach@u-cergy.fr
2
Département de Mathématiques, Université d’Evry-Val
d’Essonne, Bd François
Mitterrand, 91025
Evry Cedex,
France
dasha.loukianova@univ-evry.fr
Received:
29
November
2010
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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