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

Key Points

• The aim is to derive exact solutions for probability distributions and moments from coupled Langevin equations with variable coefficients.
• Analyzed two coupled Langevin equations with Gaussian white noise influences.
• Derived probability density functions and generalized n-moments analytically.
• Performed simulations to evaluate time-dependent diffusion coefficients with exponential decays.
• Exact solutions for ordinary n-moments were derived from power-law drift and diffusion coefficients.
• Analytical and simulation results showed distinct behaviors for varying diffusion coefficients.