Averaging of Noisy Nonlinear Systems with Rapidly Oscillating and Decaying Components

We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the...

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Bibliographic Details
Published in:Nonlinear dynamics 2004-06, Vol.36 (2-4), p.329-347
Main Authors: Namachchivaya, N. Sri, Van Roessel, Henry J.
Format: Article
Language:English
Subjects:
Markov processes
Martingales
Nonlinear systems
Springs (elastic)
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Summary:We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.
ISSN:0924-090X
1573-269X
DOI:10.1023/B:NODY.0000045523.94770.05