Average and deviation for slow-fast stochastic partial differential equations

2009/04/09 by Wang, W., Roberts, A. J. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0904.1462

Abstract

Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any Lipschitz assumption on the slow modes. The rate of convergence in probability is obtained as a byproduct. Importantly, the deviation between the original equation and the averaged equation is also studied. A martingale approach proves that the deviation is described by a Gaussian process. This gives an approximation to errors of O(\e) instead of O(√(\e)) attained in previous averaging.

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