The walk on moving spheres: a new tool for simulating Brownian motion's exit time from a domain

Abstract : In this paper we introduce a new method for the simulation of the exit time and position of a $\delta$-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 $\delta$-dimensional Bessel process and the $\delta$-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.
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Madalina Deaconu, Samuel Herrmann, Sylvain Maire. The walk on moving spheres: a new tool for simulating Brownian motion's exit time from a domain. 9th IMACS Seminar on Monte Carlo Methods (MCM), Jul 2013, Annecy le Vieux, France. pp.28-38, ⟨10.1016/j.matcom.2015.07.004⟩. ⟨hal-00931816v2⟩

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