Monte Carlo estimates of the solution of a parabolic equation and its derivatives made by solving stochastic differential equations

摘要

In this paper a method of estimation of both the solution to a parabolic boundary value problem and its derivatives with respect to parameters and spatial variables is proposed. The method uses a probability representation of a solution of a parabolic equation in the form of a functional of a diffusion process. This process is the solution of a system of stochastic differential equations (SDE) corresponding to the parabolic operator. To obtain the derivatives of the solution of the parabolic boundary value problem the differentiation of the SDE system with respect to the parameters or the initial data is applied.