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
Mots-clés : Harris recurrence, polynomial ergodicity, Nummelin splitting, continuous time Markov processes, drift condition, modulated moment
@article{PS_2013__17__195_0, author = {L\"ocherbach, Eva and Loukianova, Dasha}, title = {Polynomial deviation bounds for recurrent {Harris} processes having general state space}, journal = {ESAIM: Probability and Statistics}, pages = {195--218}, publisher = {EDP-Sciences}, volume = {17}, year = {2013}, doi = {10.1051/ps/2011156}, mrnumber = {3021315}, zbl = {1296.60199}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2011156/} }
TY - JOUR AU - Löcherbach, Eva AU - Loukianova, Dasha TI - Polynomial deviation bounds for recurrent Harris processes having general state space JO - ESAIM: Probability and Statistics PY - 2013 SP - 195 EP - 218 VL - 17 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2011156/ DO - 10.1051/ps/2011156 LA - en ID - PS_2013__17__195_0 ER -
%0 Journal Article %A Löcherbach, Eva %A Loukianova, Dasha %T Polynomial deviation bounds for recurrent Harris processes having general state space %J ESAIM: Probability and Statistics %D 2013 %P 195-218 %V 17 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2011156/ %R 10.1051/ps/2011156 %G en %F PS_2013__17__195_0
Löcherbach, Eva; Loukianova, Dasha. Polynomial deviation bounds for recurrent Harris processes having general state space. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 195-218. doi : 10.1051/ps/2011156. http://www.numdam.org/articles/10.1051/ps/2011156/
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