Taboo rate and hitting time distribution of continuous-time reversible Markov chains

Abstract

The taboo rate is first defined, which satisfies with the Chapman–Kolmogorov equation. Then the differentials of hitting time distribution are expressed by many different taboo rates, which deeply reveal the intrinsic relationship between the transition rate matrix and the hitting time distribution in continuous-time reversible Markov chains. As an example, the explicit expressions of the differentials of the hitting time distribution at a single state are provided for the birth and death chain, hence the transition rate matrix can be identified. Such differentials improve the theory of statistical identification of continuous-time reversible Markov chains.