We consider random dynamical systems with slow and fast variables driven by two independent metric dynamical systems modeling stochastic noise. We establish the existence of a random inertial manifold eliminating the fast variables. If the scaling parameter tends to zero, the inertial manifold tends to another manifold which is called the slow manifold. We achieve our results by means of a fixed point technique based on a random graph transform. To apply this technique we need an asymptotic gap condition.
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Schmalfuss, B., Schneider, K.R. Invariant Manifolds for Random Dynamical Systems with Slow and Fast Variables. J Dyn Diff Equat 20, 133–164 (2008). https://doi.org/10.1007/s10884-007-9089-7
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DOI: https://doi.org/10.1007/s10884-007-9089-7