A mathematical framework for exact milestoning

TL;DR

This paper develops a rigorous mathematical framework for Exact Milestoning, an algorithm that simplifies the analysis of continuous stochastic processes by approximating them with Markov chains, providing explicit error bounds.

Contribution

It generalizes the setting of Exact Milestoning and derives explicit error bounds for the approximation of mean first passage times.

Findings

Established a mathematical foundation for Exact Milestoning.

Derived explicit error bounds for the Milestoning equation.

Enhanced understanding of the approximation accuracy in stochastic process analysis.

Abstract

We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of Exact Milestoning and give explicit error bounds for the error in the Milestoning equation for mean first passage times.