Bounding Mean First Passage Times in Population Continuous-Time Markov Chains

Abstract

We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population models is notoriously difficult since typically neither state-based numerical approaches nor methods based on stochastic sampling give efficient and accurate results. Here, we propose a technique that extends recently developed methods using semi-definite programming to determine bounds on mean first passage times. We further apply the technique to hybrid models and demonstrate its accuracy and efficiency for some examples from biology.

The pathway elaboration method for mean first passage time estimation in large continuous-time Markov chains with applications to nucleic acid kinetics

“…Efficiently quantifying the error of MFPT estimates in truncated CTMCs for exponential and non-exponential decay processes is beyond the scope of this paper. It might be possible to use some other existing work (Kuntz et al, 2019;Backenköhler, Bortolussi and Wolf, 2019).…”