Wiener-Hopf Factorization for Time-Inhomogeneous 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 Barlow et al. (1980), which treated the case of finite time-homogeneous Markov chains. Since then, several works extended the results of Barlow et al. (1980) in many directions. However, all these extensions were dealing with time-homogeneous Markov case. The first work dealing with the time-inhomogeneous situation was Bielecki et al. (2018), 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.
Keywords
Cite
@article{arxiv.1902.10850,
title = {Wiener-Hopf Factorization for Time-Inhomogeneous Markov Chains},
author = {Tomasz R. Bielecki and Ziteng Cheng and Igor Cialenco and Ruoting Gong},
journal= {arXiv preprint arXiv:1902.10850},
year = {2019}
}