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Periodic Ornstein-Uhlenbeck processes driven by Lévy processes
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 2002
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