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The Stationary Distributions of Two Classes of Reflected Ornstein–Uhlenbeck Processes

Published online by Cambridge University Press:  14 July 2016

Xiaoyu Xing*
Affiliation:
Hebei University of Technology
Wei Zhang*
Affiliation:
Central South University
Yongjin Wang*
Affiliation:
Nankai University
*
Postal address: School of Sciences, Hebei University of Technology, Beichen District, Tianjin, 300401, P. R. China. Email address: researchandcommunication@gmail.com
∗∗Postal address: School of Mathematical Sciences, Central South University, Changsha, 410075, P. R. China.
∗∗∗Postal address: School of Business, Nankai University, Tianjin, 300071, P. R. China.
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Abstract

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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.

MSC classification

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

Supported by NSF 10671052.

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