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This paper is devoted to provide a theoretical underpinning for ensembleforecasting with rapid fluctuations in body forcing and in boundary conditions.Ensemble averaging principles are proved under suitable `mixing' conditions onrandom boundary conditions and on random body forcing. The ensemble averagedmodel is a nonlinear stochastic partial differential equation, with thedeviation process (i.e., the approximation error process) quantified as thesolution of a linear stochastic partial differential equation.

Ensemble Averaging for Dynamical Systems under Fast Oscillating Random Boundary Conditions