The Inverse First-passage Time Problem as Hydrodynamic Limit of a Particle System

Abstract

We study a particle system without branching but with selection at timepoints depending on a given probability distribution on the positive real line. The hydrodynamic limit of the particle system is identified as the distribution of a Brownian motion conditioned to not having passed the solution of the so-called inverse first-passage time problem. As application we extract a Monte-Carlo method to simulate solutions of the inverse first-passage time problem.

An elementary approach to the inverse first-passage-time problem for soft-killed Brownian motion

“…In contrast to that, in the classical inverse first-passage-time problem a continuous, piecewise linear approximation in [25] yields a Monte Carlo algorithm to approximate the barrier with error bounds. While in the classical problem several methods are known to approximate the solutions numerically (see, e.g., [1,12,13,19,24,25]), the problem of obtaining numerical approximations for the solutions of the soft-killing inverse first-passagetime problem has not been treated in the literature until now. Therefore, a more detailed study has yet to be provided in order to obtain reliable results.…”