Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics
Pahlajani, Chetan D.
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https://hdl.handle.net/2142/86889
Description
Title
Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics
Author(s)
Pahlajani, Chetan D.
Issue Date
2007
Doctoral Committee Chair(s)
Sowers, Richard B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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