Exact solution for two coupled Langevin equations driven by Gaussian white noises in heterogeneous media, with time-space-dependent drift and diffusion coefficients

Exact solutions for the probability density function and generalized n-moments are obtained from two coupled Langevin equations driven by Gaussian white noises in hetero-geneous media, with time-space-dependent drift and diffusion coefficients. In particular, exact solutions for ordinary n-moments are obtained from space-dependent power-law drift and diffusion coefficients. Simulation and analytical results are also analyzed for time-dependent diffusion coefficients with exponential decays.