An averaging principle for a completely integrable stochastic Hamiltonian system

File Description SizeFormat 
Averaging-revision.pdfAccepted version230.18 kBAdobe PDFView/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



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commonsx