Abstract
Consider a stochastic differential equation of the form of a Langevin equation, but in which the noise source is not white. If it is nearly white, i.e., its autocorrelation time is short, a systematic approximation method is known. It leads to a Fokker-Planck equation with successive higher order corrections. To obtain the coefficients more explicitly, a secondary expansion may be employed. The validity of the resulting double series approximation is discussed and confronted with the various results given in the literature. In addition, an alternative approximation method is obtained using the technique for eliminating fast variables. It produces the same terms in a different sequence.
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van Kampen, N.G. Langevin-like equation with colored noise. J Stat Phys 54, 1289–1308 (1989). https://doi.org/10.1007/BF01044716
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DOI: https://doi.org/10.1007/BF01044716