One-Dimensional Parabolic Diffraction Equations: Pointwise Estimates and Discretization of Related Stochastic Differential Equations With Weighted Local Times

Miguel Martinez (1) , Denis Talay (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 TOSCA - Simuler et calibrer des modèles stochastiques

In this paper we consider one-dimensional partial differential equations of parabolic type involving a divergence form operator with a discontinuous coefficient and a transmission compatibility condition. We prove existence and uniqueness result by stochastic methods which also allow us to develop a low complexity Monte Carlo numerical resolution method. We get accurate pointwise estimates for the derivatives of the solution from which we get sharp convergence rate estimates for our stochastic numerical method.

Mots clés: Keywords: Stochastic Differential Equations; Divergence Form Operators; Euler discretization scheme; Monte Carlo methods

Domaines: Probabilités [math.PR]

Miguel Martinez, Denis Talay. One-Dimensional Parabolic Diffraction Equations: Pointwise Estimates and Discretization of Related Stochastic Differential Equations With Weighted Local Times. 2011. ⟨inria-00607967⟩