One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times

Miguel Martinez (Université Paris-Est - Marne-la-Vallée)
Denis Talay (INRIA Sophia Antipolis)


In this paper we consider one-dimensional partial differential equations of parabolic type involving a divergence form operator with a discontinuous coefficient and a compatibility transmission 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 solutionfrom which we get sharp convergence rate estimates for our stochastic numerical method.

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Pages: 1-30

Publication Date: March 29, 2012

DOI: 10.1214/EJP.v17-1905


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