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We model chaotic diffusion, in a symplectic 4D map by using the result of atheorem that was developed for stochastically perturbed integrable Hamiltoniansystems. We explicitly consider a map defined by a free rotator (FR) coupled toa standard map (SM). We focus in the diffusion process in the action, $I$, ofthe FR, obtaining a semi--numerical method to compute the diffusioncoefficient. We study two cases corresponding to a thick and a thin chaoticlayer in the SM phase space and we discuss a related conjecture stated in thepast. In the first case the numerically computed probability density functionfor the action $I$ is well interpolated by the solution of a Fokker-Planck(F-P) equation, whereas it presents a non--constant time delay respect to theconcomitant F-P solution in the second case suggesting the presence of ananomalous diffusion time scale. The explicit calculation of a diffusioncoefficient for a 4D symplectic map can be useful to understand the slowdiffusion observed in Celestial Mechanics and Accelerator Physics.

Stochastic approach to diffusion inside the chaotic layer of a resonance