On Nummelin splitting for continuous time Harris recurrent Markov processes and application to kernel estimation for multi-dimensional diffusions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Locherbach, Eva²  Loukianova, Dasha¹ 

[1] Univ Evry Essonne, Dept Math, F-91025 Evry, France

[2] Univ Paris 12, Ctr Math, Fac Sci & Technol, F-94010 Creteil, France

关键词: Harris recurrence;    Nummelin splitting;    continuous time Markov processes;    resolvents;    special functions;    additive functionals;    Chacon-Ornstein theorem;    diffusion process;    Nadaraya-Watson estimator;   

DOI  :  10.1016/j.spa.2007.09.003

来源: Elsevier

【 摘 要 】

We introduce a sequence of stopping times that allow us to study an analogue of a life-cycle decomposition for a continuous time Markov process, which is an extension of the well-known splitting technique of Nummelin to the continuous time case. As a consequence, we are able to give deterministic equivalents of additive functionals of the process and to state a generalisation of Chen's inequality. We apply our results to the problem of non-parametric kernel estimation of the drift of multi-dimensional recurrent, but not necessarily ergodic, diffusion processes. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free