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Ergodic properties of generalized Ornstein–Uhlenbeck processes

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  • Kevei, Péter

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.

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  • Kevei, Péter, 2018. "Ergodic properties of generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 156-181.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:1:p:156-181
    DOI: 10.1016/j.spa.2017.04.010
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    References listed on IDEAS

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    Cited by:

    1. Valentin Courgeau & Almut E. D. Veraart, 2022. "Likelihood theory for the graph Ornstein-Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 227-260, July.
    2. Bertoin, Jean, 2019. "Ergodic aspects of some Ornstein–Uhlenbeck type processes related to Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1443-1454.
    3. Behme, Anita & Di Tella, Paolo & Sideris, Apostolos, 2024. "On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

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