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

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