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

Eva Löcherbach and Dasha Loukianova

Stochastic Processes and their Applications, 2008, vol. 118, issue 8, 1301-1321

Abstract: 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.

Keywords: Harris; recurrence; Nummelin; splitting; Continuous; time; Markov; processes; Resolvents; Special; functions; Additive; functionals; Chacon-Ornstein; theorem; Diffusion; process; Nadaraya-Watson; estimator (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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