Bonesini, Ofelia (2019) Existence and uniqueness of solutions for a class of McKean-Vlasov stochastic differential equations. [Magistrali biennali]
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In this thesis we deal with a class of McKean-Vlasov Stochastic Differential Equations (MV-SDEs). MV-SDEs are more involved than classical SDEs as their coefficients dependon the law of the solution itself. They are sometimes referred to as mean-fieldSDEs and were first studied by McKean inA class of Markov Process associ-ated with non linear parabolic equations(1966). These equations describe thelimiting behaviour of individual particles having diffusive dynamics and whichinteract with each other in a ”mean field” sense.In this thesis, we are interested in showing existence and uniqueness of solu-tions for a class of MV-SDEs that arise in the study of the Large DeviationPrinciple for weakly interacting Itˆo diffusions. One way of proving limit theo-rems of this type is through the so-called weak convergence approach, whichrequires, besides tightness and identification of the limit, uniqueness of solu-tions for a controlled version of the limit model.
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