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最近新作--On the transition law of tempered stable Ornstein-Uhlenbeck processes
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Zhang Shibin, Zhang Xinsheng. On the transition law of tempered stable Ornstein-Uhlenbeck processes. Journal of Applied Probability 2009, 46(3): 721-731.
Abstract
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. And
in distribution, the compound Poisson random variable is equal to a sum of
Poisson-distributed number positive random variables, which are independent
identically distributed and have a common specified density function. Based
on the representation of the stochastic integral, we proved that the transi-
tion distribution of the tempered stable Ornstein-Uhlenbeck process is self-
decomposable and the transition density is a C∞-function.
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. And
in distribution, the compound Poisson random variable is equal to a sum of
Poisson-distributed number positive random variables, which are independent
identically distributed and have a common specified density function. Based
on the representation of the stochastic integral, we proved that the transi-
tion distribution of the tempered stable Ornstein-Uhlenbeck process is self-
decomposable and the transition density is a C∞-function.
Keywords: Levy process; Tempered stable; Process of Ornstein-Uhlenbeck type;
self-decomposability
self-decomposability
https://blog.sciencenet.cn/blog-116301-233032.html
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