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A second-order algorithm for the numerical integration of colored-noise stochastic processes is presented. It goes beyond recent efforts in this direction that are really only 3/2 order. Generation of the noise for this algorithm requires the generation of two uniformly distributed random numbers at each integration step. Some of the earlier algorithms require four, or if they also only use two, they do so without requiring all cross correlations to hold up to second order as in the algorithm presented here. Several numerical results are presented that demonstrate the improvement over the well-known first-order algorithm.
Ronald F. Fox (Fri,) studied this question.