Ergodic properties of generalized Ornstein–Uhlenbeck processes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2018Embargo end date: 01 Jan 2016 Hungary English Publisher:Elsevier BVJournal:Stochastic Processes and their Applications, volume 128, pages 156-181 (issn: 0304-4149,

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Authors: Kevei, Péter;

doi: 10.1016/j.spa.2017.04.010 , 10.48550/arxiv.1606.01232

arXiv: 1606.01232

Ergodic properties of generalized Ornstein–Uhlenbeck processes

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Abstract

We investigate ergodic properties of generalized Ornstein--Uhlenbeck processes. In particular, we provide sufficient conditions for ergodicity, and for subexponential and exponential convergence to the invariant probability measure. We use the Foster--Lyapunov method. The drift conditions are obtained using the explicit form of the generator of the continuous process. In some special cases the optimality of our results can be shown.

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Hungary

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Keywords

generalized Ornstein-Uhlenbeck processes, QA Mathematics / matematika, petite set, Probability (math.PR), Stochastic ordinary differential equations (aspects of stochastic analysis), exponential / subexponential ergodicity, 60J25, FOS: Mathematics, Continuous-time Markov processes on general state spaces, Foster-Lyapunov technique, Mathematics - Probability

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