On the variance of the estimate of the functional of the diffusion process in a domain with a reflecting bounry
S.A. Gusev1,2
1Institute Computational Mathematics and Mathematical Geophysics Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State Technical University, Novosibirsk, Russia
Keywords: diffusion process, variance of the Monte Carlo method estimation, stochastic differential equations, reflecting bounry, Euler method
Abstract
The estimation of the functional of the diffusion process in a domain with a reflecting bounry, which is obtained on the basis of numerical modeling of its trajectories, is considered. The value of this functional coincides with the solution at a given point of a bounry value problem of the third kind for a parabolic equation. A formula is obtained for the limiting value of the variance of this estimate under decreasing step in the Euler method. To reduce the variance of the estimate, a transformation of the bounry value problem is used, similar to the one that was previously proposed in the case of an absorbing bounry.
|
