Journal
JOURNAL OF APPLIED PROBABILITY
Volume 46, Issue 3, Pages 721-731Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0021900200005842
Keywords
Levy process; tempered stable; Ornstein-Uhlenbeck-type process; self-decomposability
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Funding
- Natural Science Foundation of China [10671037, 10901100]
- Science Foundation of Shanghai Educational Committee [06FZ035]
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In this paper, a stochastic integral of Ornstein-Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random variables, which are independent and identically distributed and have a common specified density function. Based on the representation of the stochastic integral, we prove that the transition distribution of the tempered stable Ornstein-Uhlenbeck process is self-decomposable and that the transition density is a C-infinity-function.
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