Damped stochastic system driven by colored noise: analytical solution by a path integral approach

We consider the nonlinear non-Markovian stochastic process associated with the damped nonlinear dynamical system driven by Ornstein-Uhlenbeck noise. An approximate Fokker-Planck-type equation governing the above stochastic process is derived using the path-integral approach. The stationary probability density function (SPDF) of the above process is then computed using the matrix continued fraction method. The SPDF compares favorably with the corresponding digital simulation results obtained by us.