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An efficient method is presented as a means of an approximate, analytictime-dependent solution of the Fokker-Planck equation (FPE) for the Langevinmodel subjected to additive and multiplicative noise. We have assumed that thedynamical probability distribution function has the same structure as the exactstationary one and that its parameters are expressed in terms of first andsecond moments, whose equations of motion are determined by the FPE. Modelcalculations have shown that dynamical distributions in response to appliedsignal and force calculated by our moment method are in good agreement withthose obtained by the partial difference equation method. As an application ofour method, we present the time-dependent Fisher information for theinverse-gamma distribution which is realized in the FPE includingmultiplicative noise only.

A moment approach to analytic time-dependent solutions of the Fokker-Planck equation with additive and multiplicative noise