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An averaging principle for a completely integrable stochastic Hamiltonian system
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Averaging-revision.pdf | Accepted version | 230.18 kB | Adobe PDF | View/Open |
Title: | An averaging principle for a completely integrable stochastic Hamiltonian system |
Authors: | Li, X-M |
Item Type: | Journal Article |
Abstract: | We investigate the effective behaviour of a small transversal perturbation of order epsilon to a completely integrable stochastic Hamiltonian system, by which we mean a stochastic differential equation whose diffusion vector fields are formed from a completely integrable family of Hamiltonian functions Hi, i = 1, ..., n. An averaging principle is shown to hold and the action component of the solution converges, as epsilon → 0, to the solution of a deterministic system of differential equations when the time is rescaled at 1/epsilon. An estimate for the rate of the convergence is given. In the case when the perturbation is a Hamiltonian vector field, the limiting deterministic system is constant in which case we show that the action component of the solution scaled at 1/epsilon2 converges to that of a limiting stochastic differentiable equation. |
Issue Date: | 1-Apr-2008 |
URI: | http://hdl.handle.net/10044/1/54115 |
DOI: | https://dxd.doi.org/10.1088/0951-7715/21/4/008 |
ISSN: | 0951-7715 |
Start Page: | 803 |
End Page: | 822 |
Journal / Book Title: | Nonlinearity |
Volume: | 21 |
Copyright Statement: | © 2008 IOP Publishing Ltd and London Mathematical Society |
Keywords: | 0102 Applied Mathematics General Mathematics |
Notes: | mrclass: 60H10 (34C29 34F05 37H10 37J35 58J65) mrnumber: 2399826 mrreviewer: Kiyomasa Narita |
Article Number: | 4 |
Appears in Collections: | Pure Mathematics Faculty of Natural Sciences |