Solving SDE's numerically to estimate parametric derivatives of the solution to a parabolic boundary value problem with a Neumann boundary condition

In this paper, a parabolic boundary value problem with a Neumann boundary condition is considered. The diffusion process with reflection from the boundary corresponds to the boundary problem. A statistical method to estimate the solution and parametric derivatives of the considered problem is proposed. This method is based on solving SDE's by the Euler method. The order of convergence of the obtained estimates is established. The results of numerical computations are presented.