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CREATED:20240411T204952Z
LAST-MODIFIED:20240429T181640Z
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SUMMARY:PhD Dissertation Defense: Mr. Dan Noelck
DESCRIPTION:Contraction Rates For McKean-Vlassov Stochastic Differential Equations\nMr. Dan Noelck\nUniversity of Wisconsin-Milwaukee \nThis 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. \nAdvisor: Prof. Chao Zhu \nCommittee Members:\nProfs. Lijing Sun\, Jeb Willenbring\, Richard Stockbridge\, and Peter Hinow
URL:https://uwm.edu/math/event/phd-dissertation-defense-mr-dan-noelck/
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