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

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Abstract

Processes of Ornstein-Uhlenbeck type on Rd are analogues of the Ornstein-Uhlenbeck process on Rd 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 R1. © 1984.

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Sato, K. iti, & Yamazato, M. (1984). Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type. Stochastic Processes and Their Applications, 17(1), 73–100. https://doi.org/10.1016/0304-4149(84)90312-0

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