Stochastic Fluid Model with Jumps: The Bounded Model

As one of the important hybrid models, stochastic fluid models (SFMs, in short) have many applications. In this work, we discuss a class of SFMs modulated by Markovian chain with lower and upper jumps, where the fluid level has a positive upper bound and a lower bound zero. The joint limiting distribution of the buffer level and the environment state is expressed by a series of differential equations. An example is give to illustrate the theory obtained.