A note on Wiener-Hopf factorization for Markov Additive processes

TL;DR

This paper establishes the Wiener-Hopf factorization for Markov Additive processes and derives related theorems, providing new tools for analyzing their probabilistic structure and ladder processes.

Contribution

It introduces the Wiener-Hopf factorization and related theorems specifically for Markov Additive processes, extending classical results to this broader class.

Findings

Proved Wiener-Hopf factorization for Markov Additive processes

Derived Spitzer-Rogozin theorem for this class

Obtained Kendall's formula and Fristedt representation

Abstract

We prove the Wiener-Hopf factorization for Markov Additive processes. We derive also Spitzer-Rogozin theorem for this class of processes which serves for obtaining Kendall's formula and Fristedt representation of the cumulant matrix of the ladder epoch process. Finally, we also obtain the so-called ballot theorem.