Estimation of derivatives with respect to parameters of a functional of a diffusion process moving in a domain with absorbing boundary

In this paper, a statistical method for estimation of derivatives with respect to parameters of a functional of a diffusion process moving in a domain with absorbing boundary is proposed. The considered functional defines the probability representation of the solution of the corresponding parabolic first boundary value problem. The problem posed is solved by the numerical solution of stochastic differential equations (SDE) by the Euler method. The evaluation of an error of the proposed method is derived, and estimations of variance of the obtained parametric derivatives are given. Some numerical results are presented.