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

Author

Listed:
  • Jan Pedersen

    (University of Aarhus)

  • Ken-Iti Sato

    (Ken-Iti Sato)

Abstract

The class I(c) of stationary distributions of periodic Ornstein–Uhlenbeck processes with parameter c driven by Lévy 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 Lm are discussed.

Suggested Citation

  • Jan Pedersen & Ken-Iti Sato, 2005. "The Class of Distributions of Periodic Ornstein–Uhlenbeck Processes Driven by Lévy Processes," Journal of Theoretical Probability, Springer, vol. 18(1), pages 209-235, January.
    • Handle: RePEc:spr:jotpro:v:18:y:2005:i:1:d:10.1007_s10959-004-2595-1
    DOI: 10.1007/s10959-004-2595-1
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    Cited by:

    1. Giovanni Conforti & Tetiana Kosenkova & Sylvie Rœlly, 2019. "Conditioned Point Processes with Application to Lévy Bridges," Journal of Theoretical Probability, Springer, vol. 32(4), pages 2111-2134, December.

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