ON THE VARIANCE OF ESTIMATION OF DIFFUSION PROCESS IN A DOMAIN WITH A REFLECTING BOUNDARY

Author (s) : P.Sridhar, A.Anandhu, R.Prabhu, K.Nivetha

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Abstract :
Estimation of a diffusion process in a domain with a reflecting boundary is obtained by numerical modeling of its trajectories. The functional coincides with the solution at a given point of a boundary value problem of the third kind for a parabolic equation. A formula is obtained for the limiting value of the variance of this estimation with decreasing step size in the Euler method. To reduce the variance of the estimation, a transformation of the boundary value problem is used, which is similar to one previously proposed in the case of an absorbing boundary. This paper is devoted to studying the variance of a statistical estimate of the solution of a boundary value problem of the third kind for a parabolic equation. Such estimates are a result of numerical simulation of trajectories of diffusion processes reflected at the domain boundary in the direction of the inward-pointing normal.

Keywords : Diffusion process, variance of Monte Carlo method estimation, stochastic differential equations, reflecting boundary, Euler method.

Conference Date : 30/08/2019

Pages : 223

Paper ID : 19214