一类马氏调节反射跳扩散过程的平稳性（英文）

Stationarity of a Class of Markov-Modulated Reflected Jump Diffusion Processes

本文拓展文献[1]的马氏调节反射布朗运动模型到马氏调节反射跳-扩散过程,其中跳元素被表述为一个马氏调节复合泊松过程.我们主要计算有关该马氏调节反射跳-扩散过程的平稳分布.我们用一个具有两状态例子通过合适的边界条件来说明如何求解平稳分布所满足的积分-微分方程组.最后,作为一个特殊情况,我们给出无马氏调节反射-扩散过程的平稳分布.

In this paper, we extend the previous Markov-modulated reflected Brownian motion model discussed in [1] to a Markowmodulated reflected jump diffusion process, where the jump component is described as a Markov-modulated compound Poisson process. We compute the joint stationary distribution of the bivariate Markov jump process. An abstract example with two states is given to illustrate how the stationary equation described as a system of ordinary integro- differential equations is solved by choosing appropriate boundary conditions. As a special case, we also give the sationary distribution for this Markov jump process but without Markovian regime- switching.