The Systematic Approximation and the Systematic Adiabatic Approximation for the Stochastic Systems Driven by O-U Noises

In this paper, we generalize the systematic approximation and the systematic adiabatic approximation developed by G. Schöner and H.aken^1,2] to the stochastic systems driven by O-U noises. After eliminating the fast variables st, we introduce a new family of stochastic processes K_t^(υ) (υ≥2) in the equations for the order parameters vt. A typical model serves to illustrate how to derive the equation for the order parameter and how to calculate the statistical properties of the new stochastic processes K_t^(υ) (υ≥2). Some significant discussions and conclusions are given in Sec. V.