The walk on moving spheres: a new tool for simulating Brownian motion's exit time from a domain
Probability
2015-10-19 v2
Abstract
In this paper we introduce a new method for the simulation of the exit time and position of a -dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as well as inversion of complicated series. The idea is to use the connexion between the -dimensional Bessel process and the -dimensional Brownian motion thanks to an explicit Bessel hitting time distribution associated with a particular curved boundary. This allows to build a fast and accurate numerical scheme for approximating the hitting time. Numerical comparisons with existing methods are performed.
Cite
@article{arxiv.1401.3695,
title = {The walk on moving spheres: a new tool for simulating Brownian motion's exit time from a domain},
author = {Madalina Deaconu and Samuel Herrmann and Sylvain Maire},
journal= {arXiv preprint arXiv:1401.3695},
year = {2015}
}