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The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation

MPS-RR 2003-12
June 2003




The Class of Distributions of Periodic Ornstein-Uhlenbeck Processes Driven by Lévy Processes

by: Jan Pedersen, Ken-iti Sato

Abstract

The class $I(c)$ of stationary distributions of periodic Ornstein-Uhlenbeck processes with parameter $c$ driven by Léevy processes is analyzed. A characterization of $I(c)$ analogous to a well-known characterization of the selfdecomposable distributions is given. The relations between $I(c)$ for varying values of $c$ and the relations with the class of selfdecomposable distributions and with the nested classes $L_m$ are discussed.

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