A note on Wiener-Hopf factorization for Markov additive processes (Q457101)

This paper discusses Wiener-Hopf factorization for a class of Markov additive processes (MAPs). On one hand, MAPs play an important role in many application areas in applied probability, such as queues, insurance risk, finance and so forth; on the other hand, a MAP is a natural generization of a Lévy process. The authors give a short proof of the Wiener-Hopf factorization based on the Markov property and additivity, express the terms of the Wiener-Hopf factorization directly in terms of the basic data of the process, derive the Spitzer-Rogozin theorem and present the ballot theorem.