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Description
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 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois