C:/Users/Aaron Peterson/Desktop/jcms/V8/4Issue/CMSV8-4-11/CMSV8-4-11.dvi
نویسنده
چکیده
where X t ∈Rn, and Y ε t ∈Rm are variables in vector spaces and Wt is a standard ddimensional Wiener process. a(·)∈Rn, B(·)∈Rm, σ(·)∈Rn×Rd and C(·)∈Rm×Rd are all functions of O(1) magnitude. Systems in the form of (1.1) arise from a wide range of applications including chemical kinetics, material sciences, fluid dynamics, and finance. We have assumed that the phase space can be decomposed into slow degrees of freedom x and fast degrees of freedom y. Under appropriate assumptions on B(·) and C(·), the dynamics for Y ε t with X t =x fixed is ergodic with a unique invariant measure μx(dy). In this case, the Principle of Averaging has been proved such that in the limit of ε→0, X s converges to a stochastic differential equation of the following form:
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