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On transient Markov processes of Ornstein-Uhlenbeck type

Published online by Cambridge University Press:  22 January 2016

Kouji Yamamuro
Kouji Yamamuro*
Affiliation:
Konan Women’s Junior College, Takaya-cho, Konan 483, Japan
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Abstract.

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For Hunt processes on Rd, strong and weak transience is defined by finiteness and infiniteness, respectively, of the expected last exit times from closed balls. Under some condition, which is satisfied by Lévy processes and Ornstein-Uhlenbeck type processes, this definition is expressed in terms of the transition probabilities. A criterion is given for strong and weak transience of Ornstein-Uhlenbeck type processes on Rd, using their Lévy measures and coefficient matrices of linear drift terms. An example is discussed.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 149 , March 1998 , pp. 19 - 32
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

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