# Efficient Low-Order Approximation of First-Passage Time Distributions

## TL;DR

This paper introduces an efficient method for approximating first-passage time distributions in reaction processes by reducing the problem to a set of coupled differential equations, enabling practical computation for complex systems.

## Contribution

It presents a novel low-order approximation technique that transforms intractable first-passage time calculations into manageable differential equations, applicable to various reaction models.

## Key findings

- Accurately approximates first-passage time distributions in epidemic and trimerisation models.
- Shows good agreement with stochastic simulations across tested examples.
- Reduces computational complexity by scaling with the number of species.

## Abstract

We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem for an auxiliary observation process. The solution can be approximated efficiently by solving a closed set of coupled ordinary differential equations (for the low-order moments of the process) whose size scales with the number of species. We apply it to an epidemic model and a trimerisation process, and show good agreement with stochastic simulations.