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By use of an adiabatic elimination procedure and a time scaling t^=^-1/2t, where denotes the correlation time of colored noise (t), one arrives at a novel colored-noise approximation which is exact both for =0 and =. The theory is implemented for one-dimensional flows of the type x \. =f (x) +g (x) (t). The approximation has the form of a Smoluchowski dynamics which is valid in regions of state space for which the damping (x, ) =^-1/2-^1/2f'1 (g'/g) f is positive and large; and times t^1/2/ (x, ). This novel Smoluchowski dynamics combines the advantageous features of a recent decoupling theory that does not restrict the value of, together with those occurring in the small-correlation-time theory due to Fox. The approximative theory is applied to a nonlinear model for a dye laser driven by multiplicative noise. Excellent agreement for the stationary probability is obtained between numerical exact solution and the novel approximative theory.
Jung et al. (Fri,) studied this question.