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Title:Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics
Author(s):Pahlajani, Chetan D.
Doctoral Committee Chair(s):Sowers, Richard B.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:We construct here certain perturbed test functions for stochastic averaging of a noisy planar Hamiltonian system containing a homoclinic orbit. The noise is assumed to be small and have skewness at the homoclinic orbit. Following Sowers, we center our efforts on a singular perturbations problem in a boundary layer near the homoclinic orbit. At the heart of this analysis is the solution of a set of heat equations, coupled through their boundary data. We identify the glueing conditions, which are sufficient conditions ensuring solvability of the above problem. Probabilistically, the glueing conditions give the relative likelihoods, in the averaged picture, of diffusing into the various regions of phase space when one starts at the homoclinic orbit.
Issue Date:2007
Type:Text
Language:English
Description:91 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.
URI:http://hdl.handle.net/2142/86889
Other Identifier(s):(MiAaPQ)AAI3290344
Date Available in IDEALS:2015-09-28
Date Deposited:2007


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