Algorithms for Brownian first passage time estimation

TL;DR

This paper introduces algorithms for estimating Brownian first passage times, demonstrating exact solutions in certain cases and competitive performance in more complex scenarios, advancing computational methods in stochastic processes.

Contribution

It presents a novel algorithm that provides exact mean first passage times for linear potentials and performs well for nonlinear and higher-dimensional cases.

Findings

Exact MFPT for linear potentials in 1D regardless of lattice spacing.

Algorithm outperforms or rivals Langevin-based estimates in complex scenarios.

Numerical evidence supports the algorithm's effectiveness in various potentials.

Abstract

A class of algorithms in discrete space and continuous time for Brownian first passage time estimation is considered. A simple algorithm is derived that yields exact mean first passage times (MFPT) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time, continuous space) estimates.