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An averaging principle for integrable stochastic Hamiltonian systems
preprint
posted on 2006-10-17, 08:18 authored by Xue-Mei LiConsider a stochastic differential equation whose diffusion vector fields are
formed from an integrable family of Hamiltonian functions Hi, i = 1, . . . n. We investigate
the effect of a small transversal perturbation of order to such a system. An averaging
principle is shown to hold for this system and the action component of the solution converges,
as ! 0, to the solution of a deterministic system of differential equations when
the time is rescaled at 1/ . An estimate for the rate of the convergence is given. In the
case when the limiting deterministic system is constant we show that the action component
of the solution scaled at 1/ 2 converges to that of a limiting stochastic differentiable
equation.
History
School
- Science
Department
- Mathematical Sciences
Pages
246205 bytesPublication date
2006Notes
This is a pre-print.Language
- en