A Khasminskii type averaging principle for stochastic reaction–diffusion equations

= g(Xf (t), Y8(t)), Y8(O) y e I~k for some parameter 0 0. But in applications that is more interesting is the behavior of X, (t) for t in intervals of order e-1 or even larger. Actually, it is indeed on those time scales that the most significant changes happen, such as exit from the neighborhood of an equilibrium point or of a periodic trajectory. With the natural time scaling t F t/E, if we set XE(t) := Xe(t/s) and ', (t) := Y(t/s), (1.1) can be rewritten as dX, (t) = b(X,. (t), Y(t)), Xe(O) = x E Rn, (1.2) dd.t. 1 dtye YY I Y g Oro (t), Y,, (0), F (0)= y E R'k

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