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A wide class of nonlinear Langevin equations with drift and diffusioncoefficients separable in time and space driven by the Gaussian white noise isanalyzed in terms of a generalized n-moment. We show the system may presentergodic property, a key property in statistical mechanics, forspace-time-dependent drift and diffusion coefficients. A generalized Einsteinrelation is also obtained. Besides, we show that the first two generalizedmoments and variance are useful to describe the drift and fluctuations of thesystem.

Broad class of nonlinear Langevin equations with drift and diffusion  cofficients separable in time and space: Generalized n-moment, ergodicity,  Einstein relation and fluctuations of the system