Convergence of switching reward processes

Abstract

We study the convergence in the Skorokhod J-topology of switching reward processes constructed by sums of conditionally independent random variables or by processes with conditionally independent increments on the trajectories of switching processes. In the case where a switching process satisfies conditions of the averaging principle type and is switched by some asymptotically mixing Markov process, the convergence of the switching reward process to a nonhomogeneous process with independent increments is studied. Some applications to the analysis of reward processes in queueing models are considered.