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

Part of: Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Xiaoyu Xing ,
Wei Zhang  and
Yongjin Wang
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: [email protected]
∗∗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.

Keywords

Ornstein–Uhlenbeck processreflected processMarkov-modulated processstationary distribution

MSC classification

Secondary: 91B70: Stochastic models
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 3 , September 2009 , pp. 709 - 720
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

Supported by NSF 10671052.

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