Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Pahlajani, Chetan D.

Contributors dc:contributor

• Sowers, Richard B.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3290344

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86889