Pathwise Regularisation of McKean-Vlasov Equations with Singular Interaction Kernels
In ’07, Davie demonstrated that uniqueness of solutions to an otherwise ill-posed ODE could be restored by the addition of almost any Brownian trajectory. This represents an analytic regularisation by noise result, in contrast to earlier works of Krylov, Veretennikov et al in which regularisation was obtained by averaging over Brownian trajectories. Recently a number of authors have developed this analytic approach into a wider theory of pathwise regularisation, using the theory of averaged fields and non-linear Young integrals. In this talk I will discuss an extension of this approach to generalised McKean—Vlasov equations with singular interaction kernels. Joint work with F. Harang, University of Oslo.
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