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arXiv · 0903.1375

Slow manifold and averaging for slow-fast stochastic differential system

W. Wang·A. J. Roberts
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Abstract

We consider multiscale stochastic dynamical systems. In this article an \emph{intermediate} reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially attracting slow manifold reduced system is derived to errors of $\mathcal{O}(ε)$. Second, averaging derives an autonomous deterministic system up to errors of $\mathcal{O}(\sqrtε)$. Then an intermediate reduced model, which is an autonomous deterministic system driven by white noise up to errors of $\mathcal{O}(ε)$, is derived using a martingale approach to account for fluctuations about the averaged system. This intermediate reduced model has a simpler form than the reduced model on the stochastic slow manifold.

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W. Wang, A. J. Roberts. 2009-03-07. Slow manifold and averaging for slow-fast stochastic differential system. https://arxiv.org/abs/0903.1375

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