Digital modeling of stochastic differential equations with absorbing boundaries

The well-known methods of modeling stochastic differential equations are extended to the case of a limited range of equations with absorption on the regular part of the boundary. Direct application of conventional methods is shown to result in a very significant decrease in the rate of convergence of the solutions to accurate ones as the quantification step reduces. A variety of the method is proposed whereby this disadvantage is eliminated. Numerical examples are provided.