A Note on First Passage Time Densities for Stochastic Simulation of Diffusion

Abstract

This brief note extends our working paper [1]. A central claim in [1] is that the first passage time densities in 1-3 dimensions have upper bounds that allow the implementation of efficient von Neumann rejection schemes for generating random first passage times. This approach was adopted, among other methods, in [4]. The claim mentioned above was not proved in [1]. This note attempts to close this gap using the arguments provided in [2].