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Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type

Author

Listed:
  • Sato, Ken-iti
  • Yamazato, Makoto

Abstract

Processes of Ornstein-Uhlenbeck type on d are analogues of the Ornstein-Uhlenbeck process on d with the Brownian motion part replaced by general processes with homogeneous independent increments. The class of operator-selfdecomposable distributions of Urbanik is characterized as the class of limit distributions of such processes. Continuity of the correspondence is proved. Integro-differential equations for operator-selfdecomposable distributions are established. Examples are given for null recurrence and transience of processes of Ornstein-Uhlenbeck type on 1.

Suggested Citation

  • Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
    • Handle: RePEc:eee:spapps:v:17:y:1984:i:1:p:73-100
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