Wiener-Hopf Factorization for Time-Inhomogeneous Markov Chains

We consider a passage time of an additive functional of a Markov chain \(X\). It is of interest to find the joint distribution of this passage time and \(X\) evaluated at this passage time. Barlow et al. (1980) showed that, when \(X\) is a time-homogeneous Markov chain and the additive functional is of a specific type, the Laplace transform of the joint distribution can be obtained by solving a certain matrix equation. Such result is called Wiener-Hopf factorization for time homogeneous Markov chains. We generalize the previous result to the case of time-inhomogeneous Markov chains and the corresponding Wiener-Hopf factorization is given in terms of an operator equation. This is joint work with Tomasz R. Bielecki, Igor Cialenco and Ruoting Gong.

Event Topic

Mathematical Finance, Stochastic Analysis, and Machine Learning