One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times
Miguel Martínez, Denis Talay · Electronic Journal of Probability · 2012
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.