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

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

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arXiv · 1801.05553

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

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

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Abstract

In this paper we derive the Wiener-Hopf factorization for a finite-state time-inhomogeneous Markov chain. To the best of our knowledge, this study is the first attempt to investigate the Wiener-Hopf factorization for time-inhomogeneous Markov chains. In this work we only deal with a special class of time-inhomogeneous Markovian generators, namely piece-wise constant, which allows to use an appropriately tailored randomization technique. Besides the mathematical importance of the Wiener-Hopf factorization methodology, there is also an important computational aspect: it allows for efficient computation of important functionals of Markov chains.

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BibTeX RIS

Tomasz R. Bielecki, Igor Cialenco, Ruoting Gong, Yicong Huang. 2018-01-17. Wiener-Hopf factorization for time-inhomogeneous Markov chains and its application. https://arxiv.org/abs/1801.05553

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