Weak Averaging of Semilinear Stochastic Differential Equations with Almost Periodic Coefficients

An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged equation is obtained in distribution, as in previous works by Khasminskii and Vrkoc. This version corrects two minor errors from our paper published in J. Math. Anal. Appl. 427(1):336–364, 2015.