Rigorous Stochastic Averaging at a Center with Additive Noise

Author: Sri Namachchivaya N.  

Publisher: Springer Publishing Company

ISSN: 0025-6455

Source: Meccanica, Vol.37, Iss.1-2, 2002-01, pp. : 85-114

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Abstract

We consider a random perturbation of a two-dimensional Hamiltonian system with an isolated elliptic fixed point; that is, a center. Under an appropriate change of time, we identify a reduced stochastically-averaged model. We give a rigorous proof of averaging at the center. Our main technique is to use the martingale problem. Our formulation of the result is in a sufficiently abstract setting that it agrees with more complicated averaging results.

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