The Annals of Probability
- Ann. Probab.
- Volume 26, Number 3 (1998), 925-967.
Random perturbations of nonlinear oscillators
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.
Ann. Probab., Volume 26, Number 3 (1998), 925-967.
First available in Project Euclid: 31 May 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 34C29: Averaging method 35B20: Perturbations
Freidlin, Mark; Weber, Matthias. Random perturbations of nonlinear oscillators. Ann. Probab. 26 (1998), no. 3, 925--967. doi:10.1214/aop/1022855739. https://projecteuclid.org/euclid.aop/1022855739