Markov Additive Processes

Abstract

Markov additive processes form a rather general class of two-component stochastic processes, which include many important models such as fluid flows (both with or without Brownian components), Lévy processes, and Markov random walks. They can be used to define point processes such as the Markov modulated Poisson process, the Markovian arrival process (MAP), and Markov renewal processes. They seem particularly well suited in connection with matrix-exponential methods.