{"id":14152,"date":"2024-04-11T15:49:52","date_gmt":"2024-04-11T20:49:52","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=14152"},"modified":"2024-04-29T13:16:40","modified_gmt":"2024-04-29T18:16:40","slug":"phd-dissertation-defense-mr-dan-noelck","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/phd-dissertation-defense-mr-dan-noelck\/","title":{"rendered":"PhD Dissertation Defense: Mr. Dan Noelck"},"content":{"rendered":"

\"\"Contraction Rates For McKean-Vlassov Stochastic Differential Equations<\/h1>\n

Mr. Dan Noelck
\nUniversity of Wisconsin-Milwaukee<\/p>\n

This work focuses on the contraction rates for McKean-Vlasov stochastic differential equations (SDEs), McKean-Vlasov Stochastic differential delay equations (SDDEs), and path dependent McKean-Vlasov stochastic differential equations.
\nUnder suitable conditions on the coefficients of the SDE, this dissertation derives explicit quantitative contraction rates for the convergence in Wasserstein distances of McKean-Vlasov SDEs using the coupling method. The contraction results are then used to prove a propagation of chaos uniformly in time, which
\nprovides quantitative bounds on convergence rate of interacting particle systems, and establishes exponential ergodicity for McKean-Vlasov SDEs. The dissertation further develops suitable conditions on the coefficients of the McKean-Vlasov SDDE to obtain a contraction in Wasserstein distance using the coupling method again. These results are used to establish exponential ergodicity for McKean-Vlasov SDDEs. Last the dissertation obtains suitable conditions on the coefficients of the path dependent McKean-Vlasov SDE for a contraction in Wasserstein distance.<\/p>\n

Advisor:<\/strong> Prof. Chao Zhu<\/p>\n

Committee Members:
\n<\/strong>Profs. Lijing Sun, Jeb Willenbring, Richard Stockbridge, and Peter Hinow<\/p>\n","protected":false},"excerpt":{"rendered":"

Contraction Rates For McKean-Vlassov Stochastic Differential Equations Mr. Dan Noelck University of Wisconsin-Milwaukee This work focuses on the contraction rates for McKean-Vlasov stochastic differential equations (SDEs), McKean-Vlasov Stochastic differential delay equations (SDDEs), and path dependent McKean-Vlasov stochastic differential equations. Under …<\/p>\n","protected":false},"author":4217,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[64],"class_list":["post-14152","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-graduate-student-defenses","cat_graduate-student-defenses"],"yoast_head":"\nMathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/uwm.edu\/math\/event\/phd-dissertation-defense-mr-dan-noelck\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"PhD Dissertation Defense: Mr. Dan Noelck\" \/>\n<meta property=\"og:description\" content=\"Contraction Rates For McKean-Vlassov Stochastic Differential Equations Mr. Dan Noelck University of Wisconsin-Milwaukee This work focuses on the contraction rates for McKean-Vlasov stochastic differential equations (SDEs), McKean-Vlasov Stochastic differential delay equations (SDDEs), and path dependent McKean-Vlasov stochastic differential equations. 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