{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86889"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86889","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Pahlajani, Chetan D."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Sowers, Richard B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:01Z","date_published":"2015-09-28T15:20:01Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3290344"],"render_values":[{"text":"(MiAaPQ)AAI3290344","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86889","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Sowers, Richard B."]},{"key":"dc:creator","label":"Author","values":["Pahlajani, Chetan D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:01Z","10000-01-01","2007"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86889","(MiAaPQ)AAI3290344"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2015-09-28T15:20:01Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290344.pdf: 2285404 bytes, checksum: d62f00733473a8ae8dc9807066318b03 (MD5) Previous issue date: 2007","Embargo set by: Seth Robbins for item 88170 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","91 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007."]},{"key":"dc:title","label":"Title","values":["Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics"]}]}],"canonical_facts":{"dc:contributor":["Sowers, Richard B."],"dc:creator":["Pahlajani, Chetan D."],"dc:date":["2015-09-28T15:20:01Z","10000-01-01","2007"],"dc:description":["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.","Made available in DSpace on 2015-09-28T15:20:01Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290344.pdf: 2285404 bytes, checksum: d62f00733473a8ae8dc9807066318b03 (MD5) Previous issue date: 2007","Embargo set by: Seth Robbins for item 88170 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","91 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007."],"dc:identifier":["http://hdl.handle.net/2142/86889","(MiAaPQ)AAI3290344"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Stochastic Averaging Correctors for a Noisy Hamiltonian System With Discontinuous Statistics"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}