Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-15

April 2002

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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