Abstract
A successive approximation procedure is proposed for stochastic systems reducible to standard form with non-“white noise” perturbations. To a first approximation, the solution of the perturbed system converges to the solution of some averaged deterministic system, and to a second approximation it converges to the solution of some averaged diffusion equation. Higher approximations enable one to estimate the deviations from a diffusion process. The convergence interval depends on the properties of the deterministic solution of the first-approximation equation.
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