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Periodic Ornstein-Uhlenbeck processes driven by Lévy processes

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Jan Pedersen
Jan Pedersen*
Affiliation:
MaPhySto and University of Aarhus
*
∗ Postal address: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark. Email address: [email protected]
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Abstract

In this paper, the class of periodic Ornstein-Uhlenbeck processes is defined. It is shown that periodic Ornstein-Uhlenbeck processes are stationary Markov random fields and the class of stationary distributions is characterized. In particular, any self-decomposable distribution is the stationary distribution of some periodic Ornstein-Uhlenbeck process. As examples, gamma periodic Ornstein-Uhlenbeck processes and Gaussian periodic Ornstein-Uhlenbeck processes are considered.

Keywords

Periodic processesLévy processesOrnstein-Uhlenbeck processesself-decomposable distributions

MSC classification

Primary: 60G10: Stationary processes 60G51: Processes with independent increments; L'evy processes
Secondary: 60H05: Stochastic integrals
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 748 - 763
Copyright
Copyright © Applied Probability Trust 2002 

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