Anzeletti, L. (2024, October 24). Properties of the solution of singular SDEs with fractional noise and well-posedness for a McKean-Vlasov equation [Presentation]. Stochastik Seminar der Universität Augsburg 2024, Augsburg, Germany.
Stochastic Analysis; Regularization by noise; Stochastic Differential Equations
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Abstract:
We look at SDEs with additive fractional Brownian noise and distributional (time-dependent) drift. Well-posedness of such equations has been thoroughly studied in recent years, generally known as a phenomenon called regularization by noise . We prove existence of a density of the solution to such equations and investigate the properties thereof. In particular, the density has a certain regularity and Gaussian tails. This is used to extend results on existence and uniqueness of solutions to a convolution-type McKean-Vlasov equation. Based on joint work with Lucio Galeati, Alexandre Richard and Etienne Tanré.