Abstract
The problem of simulating phase trajectories of a diffusion process in a bounded domain is considered. For systems with zero drift the next approximate point on the phase trajectory is found as a solution of the system with coefficients frozen at the previous point by a random walk over the boundary of a small ellipsoid. Theorems on mean-square order of accuracy for such an approximation are proved. An algorithm for approximate construction of exit points from the bounded domain is given.
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