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Contents of PMS, Vol. 40, Fasc. 2,
pages 225 - 244
DOI: 10.37190/0208-4147.40.2.3
Published online 18.6.2020
 

Wiener--Hopf factorization for time-inhomogeneous Markov chains and its application

T. R. Bielecki
Igor Cialenco
Ruoting Gong
Yicong Huang

Abstract: We derive the Wiener–Hopf factorization for a finite-state time-inhomogeneous Markov chain. Considered as the first step in the direction of the Wiener–Hopf factorization for time-inhomogeneous Markov chains, this work deals only with a special, but important class of time-inhomogeneous Markovian generators, namely piecewise constant generators, which allows us to use an appropriately tailored randomization technique.

2010 AMS Mathematics Subject Classification: Primary 60J27, 60J28, 60K30, 90B05. Secondary XXXX.

Keywords and phrases: Wiener--Hopf factorization, inhomogeneous Markov chain, fluctuation theory, randomization method, additive functional.

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