A NEW APPROACH TO COMPUTING THE TRANSIENT-STATE PROBABILITIES IN TIME-INHOMOGENEOUS MARKOV CHAINS

Abstract This paper considers the computation of the transient-state probabilities in time-inhomogenous continuous-time Markov chains. We first introduce a new class of time-inhomogenous Markov chains, which is closely related to the phase-type representation of non-negative probability distributions. We show that the introduced class of Markov chains covers a wide-class of time-inhomogenous Markov chains. We then develop a computational method of the transient-state probabilities in Markov chains of this class, which is an extension of the uniformization method in time-homogeneous Markov chains. The developed computational method has a remarkable feature that the time-discretization of the generator is not necessary, as opposed to previously known methods in the literature.