WIAS Preprint No. 347, (1997)

On the mean-square approximation of a diffusion process in a bounded domain


  • Milstein, Grigori N.

2010 Mathematics Subject Classification

  • 60H10 60J15 65U05


  • mean-square approximation, random walk, exit point


The problem of simulating phase trajectories of a diffusion process in a bounded domain is considered. Unlike usual approximation of SDE when a time-discretization is exploited, here a space-discretization is recommended. 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.

Appeared in

  • Stochastics Stochastics Rep., 64 (1998), pp. 211-233

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