马氏调节反射O-U过程的平稳分布

›› 2013, Vol. 26 ›› Issue (12): 20-.

马氏调节反射O-U过程的平稳分布

杨冰

(西安电子科技大学理学院,陕西西安 710071)

出版日期:2013-12-15 发布日期:2014-01-10
作者简介:杨冰(1987—),女,硕士研究生。研究方向:随机过程与金融衍生品定价。E-mail:bingyang165@sina.cn

Stationary Distribution of the Markov-modulated Reflected O-U Process

YANG Bing

(School of Science,Xidian University,Xi'an 710071,China)

Online:2013-12-15 Published:2014-01-10

摘要/Abstract

摘要：

讨论了一类特殊随机过程,即马氏调节双边反射带跳的O-U过程。其中的参数和跳均被一个有限状态空间、连续时间的齐次不可约马氏链所调节。文中的主要目的是证明该过程的平稳分布满足一个交互积分-微分方程。尤其当,马氏链只有两个状态时,讨论交互积分-微分方程解的存在唯一性问题,并在给出合适的边界条件下进行数值说明。

关键词: 马氏调节, Ornstein-Uhlenbeck过程, 平稳分布, 积分-微分方程

Abstract:

This paper studies the reflected Markov-modulated Ornstein-Uhlenbeck process with a two sided reflection and a jump,in which the coefficient,the two boundaries and the jump are modulated by a finite state space irreducible continuous time Markov chain.It is proved that the stationary distribution of this process satisfies an interactive ordinary integro-differential equation,and the equation has unique solution where the Markov chain has two states.The numerical illustration for the stationary distribution is given by choosing appropriate boundary condition.

Key words: markov-modulated;Ornstein-Uhlenbeck process;stationary distribution;integro-differential eqution

中图分类号:

O212

杨冰. 马氏调节反射O-U过程的平稳分布[J]. , 2013, 26(12): 20-.

YANG Bing. Stationary Distribution of the Markov-modulated Reflected O-U Process[J]. , 2013, 26(12): 20-.