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

TL;DR

This paper introduces a semi-definite programming method to efficiently bound mean first passage times in population continuous-time Markov chains, addressing computational challenges in stochastic population models.

Contribution

It extends existing semi-definite programming techniques to hybrid models, providing a new approach for accurate and efficient analysis of complex stochastic systems.

Findings

Method accurately bounds mean first passage times

Demonstrates efficiency on biological population models

Applicable to hybrid stochastic models

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.