1000.
We study a class of nonlinear Ito stochastic differential equations (with possibly state dependent diffusion coefficients), in which the variables can be divided into linearly damped (slaved) variables s and linearly undamped variables
u (order parameters). We devise a systematic and constructive procedure to eliminate the slaved variables. We take explicit time and chance dependence of the slaved variables into account, the latter via a family of diffusion processes
Z
t
(v)
. These act as fluctuating coefficients of the Center Manifold
s
t=
s(u
t, t,
Z
t
(v)
(v=2, 3, ...)) and appear explicitly in the elimination procedure. We show how in the Ito calculus fluctuating and deterministic coefficients of the Center Manifold are more completely separated than in the previously treated Stratonovich case [1]. The adiabatic approximation is defined as a partial summation of the elimination expansion and the stochastic generalization of
s=0 is derived. We show how thus ambiguity of stochastic calculi is removed. Closed form summations are given in two examples. We briefly indicate the potential use of perturbation theory techniques in the systematic elimination procedure.
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