The stationary distributions of two classes of reflected Ornstein--Uhlenbeck
processes
Xing Xiaoyu, Zhang Wei, and Wang Yongjin
Source: J. Appl. Probab.
Volume 46, Number 3
(2009), 709-720.
Abstract
In this paper we consider two classes of reflected
Ornstein--Uhlenbeck (OU) processes: the reflected
OU process with jumps and the Markov-modulated reflected OU
process. We prove that their stationary distributions exist.
Furthermore, for the jump reflected OU process, the Laplace
transform (LT) of the stationary distribution is given. As for
the Markov-modulated reflected OU process, we derive an equation
satisfied by the LT of the stationary distribution.
Keywords: Ornstein--Uhlenbeck process; reflected process; Markov-modulated process; stationary distribution
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1253279847
Digital Object Identifier: doi:10.1239/jap/1253279847
Zentralblatt MATH identifier:
05611413
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