Wiener-Hopf factorization technique for time-inhomogeneous finite Markov chains

Abstract

This work contributes to the theory of Wiener-Hopf type factorization for finite Markov chains. This theory originated in the seminal paper [BRW80], which treated the case of finite time-homogeneous Markov chains. Since then, several works extended the results of [BRW80] in many directions. However, all these extensions were dealing with time-homogeneous Markov case. The first work dealing with the time-inhomogeneous situation was [BCGH18], where Wiener-Hopf type factorization for time-inhomogeneous finite Markov chain with piecewise constant generator matrix function was derived. In the present paper we go further: we derive and study Wiener-Hopf type factorization for time-inhomogeneous finite Markov chain with the generator matrix function being a fairly general matrix valued function of time.

Wiener-Hopf Factorization for Arithmetic Brownian Motion with Time-Dependent Drift and Volatility

“…We need to add that the present paper is a continuation of work towards developing Wiener-Hopf type theory for time-inhomogeneous Markov processes. The previous work in this direction is presented in [3] and [4].…”