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

A statistical method is proposed for estimating derivatives with respect to parameters of a functional of a diffusion process moving in a domain with absorbing boundary. The functional considered defines the probability representation of the solution of a corresponding parabolic first boundary-value problem. The problem posed is tackled by numerically solving stochastic differential equations (SDE) using the Euler method. An error of the proposed method is evaluated, and estimates of the variance of the resultant parametric derivatives are given. Some numerical results are presented.