Ergodic properties of generalized Ornstein–Uhlenbeck processes

Péter Kevei

Stochastic Processes and their Applications, 2018, vol. 128, issue 1, 156-181

Abstract: We investigate ergodic properties of the solution of the SDE dVt=Vt−dUt+dLt, where (U,L) is a bivariate Lévy process. This class of processes includes the generalized Ornstein–Uhlenbeck processes. 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.

Keywords: Generalized Ornstein–Uhlenbeck processes; Foster–Lyapunov technique; Exponential / subexponential ergodicity; Petite set (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:1:p:156-181

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DOI: 10.1016/j.spa.2017.04.010

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