{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/116215"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/116215","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Duality for nonlinear filtering","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","abstract_has_math":false,"creators":["Kim, Jin Won"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Mehta, Prashant G","Hajek, Bruce","Raginsky, Maxim","Dey, Partha S"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-08","date_published":"2022-08","updated_at":"2026-07-22T22:24:55Z","subjects":["Stochastic filtering","Backward stochastic differential equations","Duality"],"languages":["en","eng"],"rights":["Copyright 2022 Jin Won Kim"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/116215","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mehta, Prashant G","Hajek, Bruce","Raginsky, Maxim","Dey, Partha S"]},{"key":"dc:creator","label":"Author","values":["Kim, Jin Won"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-08","2022-07-15"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"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":["Stochastic filtering","Backward stochastic differential equations","Duality"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Jin Won Kim"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/116215"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","The student, Jin Won Kim, accepted the attached license on 2022-07-11 at 17:47.","The student, Jin Won Kim, submitted this Dissertation for approval on 2022-07-11 at 17:48.","This Dissertation was approved for publication on 2022-07-15 at 10:43.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18238 on 2022-11-15 at 17:38:50","This thesis is concerned with the stochastic filtering problem for a hidden Markov model (HMM) with the white noise observation model. For this filtering problem, we make three types of original contributions: (1) dual controllability characterization of stochastic observability, (2) dual minimum variance optimal control formulation of the stochastic filtering problem, and (3) filter stability analysis using the dual optimal control formulation. For the first contribution of this thesis, a backward stochastic differential equation (BSDE) is proposed as the dual control system. The observability (detectability) of the HMM is shown to be equivalent to the controllability (stabilizability) of the dual control system. For the linear-Gaussian model, the dual relationship reduces to classical duality in linear systems theory. The second contribution is to transform the minimum variance estimation problem into an optimal control problem. The constraint is given by the dual control system. The optimal solution is obtained via two approaches: (1) by an application of maximum principle and (2) by the martingale characterization of the optimal value. The optimal solution is used to derive the nonlinear filter. The third contribution is to carry out filter stability analysis by studying the dual optimal control problem. Two approaches are presented through Chapters 7 and 8. In Chapter 7, conditional Poincar\\'e inequality (PI) is introduced. Based on conditional PI, various convergence rates are obtained and related to literature. In Chapter 8, the stabilizability of the dual control system is shown to be a necessary and sufficient condition for filter stability on certain finite state space model."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Duality for nonlinear filtering"]}]}],"canonical_facts":{"dc:contributor":["Mehta, Prashant G","Hajek, Bruce","Raginsky, Maxim","Dey, Partha S"],"dc:creator":["Kim, Jin Won"],"dc:date":["2022-08","2022-07-15"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","The student, Jin Won Kim, accepted the attached license on 2022-07-11 at 17:47.","The student, Jin Won Kim, submitted this Dissertation for approval on 2022-07-11 at 17:48.","This Dissertation was approved for publication on 2022-07-15 at 10:43.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18238 on 2022-11-15 at 17:38:50","This thesis is concerned with the stochastic filtering problem for a hidden Markov model (HMM) with the white noise observation model. For this filtering problem, we make three types of original contributions: (1) dual controllability characterization of stochastic observability, (2) dual minimum variance optimal control formulation of the stochastic filtering problem, and (3) filter stability analysis using the dual optimal control formulation. For the first contribution of this thesis, a backward stochastic differential equation (BSDE) is proposed as the dual control system. The observability (detectability) of the HMM is shown to be equivalent to the controllability (stabilizability) of the dual control system. For the linear-Gaussian model, the dual relationship reduces to classical duality in linear systems theory. The second contribution is to transform the minimum variance estimation problem into an optimal control problem. The constraint is given by the dual control system. The optimal solution is obtained via two approaches: (1) by an application of maximum principle and (2) by the martingale characterization of the optimal value. The optimal solution is used to derive the nonlinear filter. The third contribution is to carry out filter stability analysis by studying the dual optimal control problem. Two approaches are presented through Chapters 7 and 8. In Chapter 7, conditional Poincar\\'e inequality (PI) is introduced. Based on conditional PI, various convergence rates are obtained and related to literature. In Chapter 8, the stabilizability of the dual control system is shown to be a necessary and sufficient condition for filter stability on certain finite state space model."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/116215"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Jin Won Kim"],"dc:subject":["Stochastic filtering","Backward stochastic differential equations","Duality"],"dc:title":["Duality for nonlinear filtering"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:55Z"}