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

Eva Loecherbach 1, * Dasha Loukianova 2
* Corresponding author
1 AGM - Analyse, Géométrie et Modélisation
2 Laboratoire Analyse et Probabilités
Abstract : We introduce a sequence of stopping times that allow 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 time-continuous 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.
Keywords : Harris recurrence Nummelin splitting Continuous time Markov processes Resolvents Special functions Additive functionals Chacon-Ornstein theorem Diffusion process Nadaraya-Watson estimator
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Eva Loecherbach, Dasha Loukianova. On Nummelin splitting for continuous time Harris recurrent Markov processes and application to kernel estimation for multi-dimensional diffusions. Stochastic Processes and their Applications, Elsevier, 2008, 118 (8), pp.1301-1321. ⟨10.1016/j.spa.2007.09.003⟩. ⟨hal-00798486⟩

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