Hitting Times for Continuous-Time Imprecise-Markov Chains

TL;DR

This paper extends the concept of expected hitting times to a robust class of continuous-time Markov chains based on imprecise probabilities, providing tight bounds and a unified linear system characterization.

Contribution

It introduces a generalized framework for continuous-time imprecise-Markov chains and proves the equivalence of hitting times across different model types, along with a simple linear system for their computation.

Findings

Hitting times are equivalent across three model types.

Expected hitting times are characterized by a generalized linear system.

The approach provides tight bounds within the set of stochastic processes.

Abstract

We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work essentially constitute sets of stochastic processes. Their inferences are tight lower- and upper bounds with respect to variation within these sets. We consider three distinct types of these models, corresponding to different levels of generality and structural independence assumptions on the constituent processes. Our main results are twofold; first, we demonstrate that the hitting times for all three types are equivalent. Moreover, we show that these inferences are described by a straightforward generalization of a well-known linear system of equations that characterizes expected hitting times for traditional time-homogeneous continuous-time Markov chains.