Open Access
July 1998 Random perturbations of nonlinear oscillators
Mark Freidlin, Matthias Weber
Ann. Probab. 26(3): 925-967 (July 1998). DOI: 10.1214/aop/1022855739


Degenerate white noise perturbations of Hamiltonian systems in $R^2$ are studied. In particular, perturbations of a nonlinear oscillator with 1 degree of freedom are considered. If the oscillator has more than one stable equilibrium, the long time behavior of the system is defined by a diffusion process on a graph. Inside the edges the process is defined by a standard averaging procedure, but to define the process for all $t > 0$ one should add gluing conditions at the vertices. Calculation of the gluing conditions is based on delicate Hörmander-type estimates.


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Mark Freidlin. Matthias Weber. "Random perturbations of nonlinear oscillators." Ann. Probab. 26 (3) 925 - 967, July 1998.


Published: July 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0935.60038
MathSciNet: MR1634409
Digital Object Identifier: 10.1214/aop/1022855739

Primary: 34C29 , 35B20 , 60H10
Secondary: 35H05

Keywords: averaging principle , Hamiltonian systems , Random perturbations

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 3 • July 1998
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