Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type |
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Authors: | Ken-iti Sato Makoto Yamazato |
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Institution: | Department of Mathematics, College of Liberal Arts, Kanazawa University, Kanazawa, Japan;Department of Mathematics, Nagoya Institute of Technology, Nagoya, Japan |
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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. |
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Keywords: | infinitely divisible distribution OL distribution operator-selfdecomposable distribution limit distribution process of Ornstein-Uhlenbeck type Lévy measure |
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