Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise.

Traditionally, stochastic differential equations used in the physical sciences have involved Gaussian white noise. ' In recent times, however, white noise has been replaced by colored noise in a variety of contexts. Laser noise problems and first passage time problems have been shown to necessitate the use of colored noise instead of white noise. Even the mathematical foundations for the theory of stochastic differential equations call for colored noise if the Stratonovich perspective is adopted, as it is when physical arguments are invoked. ' In each of these contexts, many speci6c problems require numerical simulation as a component of a complete analysis. This is usually a consequence of nonlinearity and the resulting intractability in purely analytic terms. Consequently, numerical-simulation algorithms have been developed, originally for white noise, and recently for colored noise as well. The simplest type of colored noise to generate is exponentially correlated colored noise. Such noise introduces only one more parameter, the correlation time for the exponential correlation, and it is easily generated by a linear damping equation driven by white noise. Our new algorithm is for this kind of colored noise. In Sec. II we review the white-noise algorithm and the differential version of the exponentially correlated, colored-noise algorithm. In Sec. III we present the integral version of the colored-noise algorithm and demonstrate its superior properties.