The Annals of Applied Probability

A remark on random perturbations of the nonlinear pendulum

Mark Freidlin and Matthias Weber

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Abstract

We describe the long-time behavior of the nonlinear pendulum perturbed by a small noise. To derive this asymptotics, one has to consider diffusion processes on the graph corresponding to the Hamiltonian of the pendulum.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 3 (1999), 611-628.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962806

Digital Object Identifier
doi:10.1214/aoap/1029962806

Mathematical Reviews number (MathSciNet)
MR1722275

Zentralblatt MATH identifier
0960.60051

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 34C29: Averaging method 35B20: Perturbations

Keywords
Averaging principle random perturbations nonlinear pendulum

Citation

Freidlin, Mark; Weber, Matthias. A remark on random perturbations of the nonlinear pendulum. Ann. Appl. Probab. 9 (1999), no. 3, 611--628. doi:10.1214/aoap/1029962806. https://projecteuclid.org/euclid.aoap/1029962806


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References

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