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Stochastic perturbations to conservative dynamical systems on the plane. I. Convergence of invariant distributions


Author: G. Wolansky
Journal: Trans. Amer. Math. Soc. 309 (1988), 621-639
MSC: Primary 35R60; Secondary 58F11, 60J60, 93E03
DOI: https://doi.org/10.1090/S0002-9947-1988-0961604-X
MathSciNet review: 961604
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Abstract: We consider a nonlinear system on the plane, given by an oscillator with homoclinic orbits. The above system is subjected to a perturbation, composed of a deterministic part and a random (white noise) part. Assuming the existence of a finite, invariant measure to the perturbed system, we deal with the convergence of the measures to a limit measure, as the perturbation parameter tends to zero. The limit measure is constructed in terms of the action function of the unperturbed oscillator, and the strong local $ {L_2}$ convergence of the associated densities is proved.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0961604-X
Keywords: Diffusion process, perturbation, invariant distribution
Article copyright: © Copyright 1988 American Mathematical Society

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