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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Sri Namachchivaya, N., Sowers, R.B. Rigorous Stochastic Averaging at a Center with Additive Noise. Meccanica 37, 85–114 (2002). https://doi.org/10.1023/A:1019614613583
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DOI: https://doi.org/10.1023/A:1019614613583