Momenta of distribution function and kinetic equation for stochastic motion of nonlinear oscillator

Analytical approach to the study of stochastic motion of nonlinear one-dimensional system in periodic external field is developed. The ad hoc introduction of any auxiliary random parameters. The method of calculating the diffusion constant is reduced to finding a solution of the infinite system of linear inhomogeneous equations. In the limit of large values of Chirikov stochasticity parameter K the system is simplified considerably and can be described up to the terms of the order 1/(4K)sup(1/2) by the system of two equations. In this case the diffusion constant can be easily found. In the leading order in this parameter, the explicit expression for the generating function of the distribution function momenta is obtained. The diffusion type equation for coarse grained distribution function is also derived. This equation differs noticeably from the standard simple diffUsion equation. However, in the limit Qf large time its solution approaches asymptotically the Gaussian distribution