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

In this paper we introduce a new method for the simulation of the exit time and position of a $δ$-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 $δ$-dimensional Bessel process and the $δ$-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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