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

Ken-iti Sato and Makoto Yamazato

Stochastic Processes and their Applications, 1984, vol. 17, issue 1, 73-100

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.

Keywords: infinitely; divisible; distribution; OL; distribution; operator-selfdecomposable; distribution; limit; distribution; process; of; Ornstein-Uhlenbeck; type; Lévy; measure (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (30)

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