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Wiener–Hopf Factorization for Time-Inhomogeneous Markov Chains and its Application

Bielecki Tomasz R., Cialenco Igor, Gong Ruoting, Huang Yicong

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 2

225--244

We derive the Wiener–Hopf factorization for a finite-state timeinhomogeneous Markov chain. Considered as the first step in the direction of theWiener–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.