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

Madalina Deaconu (1, 2) , Samuel Herrmann (3) , Sylvain Maire (1, 4)

1 TOSCA - TO Simulate and CAlibrate stochastic models
2 Probabilités et statistiques
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]
4 LMS - Laboratoire Modélisation et Signal

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.

Mots clés: numerical algorithm; hitting time; Bessel processes

Domaines: Probabilités [math.PR]

Madalina Deaconu, Samuel Herrmann, Sylvain Maire. The walk on moving spheres: a new tool for simulating Brownian motion's exit time from a domain. Mathematics and Computers in Simulation, 2015. ⟨hal-00931816v1⟩