A Random Differential Equation based method for a d-dimensional PDE of convection-diffusion type

Abstract

We consider d−dimensional PDEs of convention-diffusion type with at most Hölder continuous coefficients. We construct an stochastic numerical method for the Monte Carlo integration of this kind of equations. The proposed approach is based on the probabilistic representation of this deterministic PDE through the solution of an associated stochastic transport equation, which remarkably can be efficiently integrated without considering the standard assumptions that typically are needed by convectional numerical integrators for solving the underlying PDE. Results on the convergence of the proposed method and details on its implementation are presented.