On the weak convergence of alternating processes

Abstract

Abstract The weak convergence of stochastic processes whose law of motion changes, is considered. The law of motion consists of two parts, the first depends on the processes' present value and the other is the input process. It is shown that if the input process is a compound Poisson process that converges weakly to Brownian motion with drift, then the alternating process converges to a diffusion process with similar law of motion.