On-the-fly Uniformization of Time-Inhomogeneous Infinite Markov Population Models

TL;DR

This paper introduces an on-the-fly uniformization method for analyzing complex time-inhomogeneous Markov population models with infinite states, dynamically focusing on the most probable states to enable practical computation.

Contribution

It proposes a novel dynamic uniformization approach that handles infinite state spaces in time-inhomogeneous Markov models, applicable to biochemical networks.

Findings

Effective approximation of infinite models demonstrated

Applicable to biochemical reaction networks

Maintains most probable states dynamically

Abstract

This paper presents an on-the-fly uniformization technique for the analysis of time-inhomogeneous Markov population models. This technique is applicable to models with infinite state spaces and unbounded rates, which are, for instance, encountered in the realm of biochemical reaction networks. To deal with the infinite state space, we dynamically maintain a finite subset of the states where most of the probability mass is located. This approach yields an underapproximation of the original, infinite system. We present experimental results to show the applicability of our technique.