Abstract:
The estimation of the functional of the diffusion process in a domain with a reflecting boundary, 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 boundary 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 boundary value problem
is used, similar to the one that was previously proposed in the case of an absorbing boundary.
Key words:diffusion process, variance of the Monte Carlo method estimation, stochastic differential equations, reflecting boundary, Euler method.
Fulltext:
PDF file (621 kB)