Simulation exacte d'Equations Différentielles Stochastiques faisant intervenir le temps local en zéro du processus inconnu

English

Séminaire Probabilités & Statistique

3/05/2012 - 14:00 Pierre Étoré (LJK / MATHFI) Salle 1 - Tour IRMA

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.

This is a joint work with Miguel Martinez, from Université Marne-la-Vallée Paris-Est.