A Unified Approach for Hitting Time of Jump Markov Type Processes

Abstract

This paper investigates the asymptotic analysis of the hitting time of Markov-type jump processes (i.e., semi-Markov, Markov, in continuous or discrete time) with a small probability of entering a non-empty terminal subset. This means that absorption is a rare event. The mean hitting time function of all four type processes obeyed the same equation. We obtain unified results of asymptotic approximation in a series scheme or, equivalently, a functional type of mean hitting time.