Stochastic PDEs and weakly interacting particle systems - Mayorcas, A (2020)
We study two problems relating to weakly interacting particle systems in the presence of exogenous noise. Part I presents a pathwise regularisation by noise result for McKean–Vlasov equations with singular interaction kernels. Using ideas from the theory of averaged fields and non-linear Young integrals we obtain well-posedness of the McKean–Vlasov systems, particle approximations and mean field convergence.