Exact Simulation of One-dimensional Stochastic Differential Equations involving the local time at zero of the unknown process

Pierre Etoré (1) , Miguel Martinez (2)

1 LJK - Laboratoire Jean Kuntzmann
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In this article we extend the exact simulation methods of Beskos et al. to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we compute the law of the skew Brownian motion with drift. The method presented in this article covers the case where the solution of the SDE with local time corresponds to a divergence form operator with a discontinuous coefficient at zero. Numerical examples are shown to illustrate the method and the performances are compared with more traditional discretization schemes.

Mots clés: Exact simulation; Skew brownian motion; One-dimensional diffusion; Local time

Domaines: Probabilités [math.PR]

Pierre Etoré, Miguel Martinez. Exact Simulation of One-dimensional Stochastic Differential Equations involving the local time at zero of the unknown process. 2012. ⟨hal-00565286v2⟩