MPS-RR 2002-15
April 2002

Periodic Ornstein-Uhlenbeck Processes

by:

Jan Pedersen

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 selfdecomposable 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.

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This paper has now been published in Journal of Applied Probability, 39, 748-763 (2002)