University of Bologna
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The usefulness of propagators and semigroups in an analytical approach to McKean-Vlasov SDEs
McKean-Vlasov SDEs are a class of Stochastic Differential Equations where the coefficients depend upon the marginals of the solution. Their study is justified by their usefulness in modeling the evolution of multi-agent systems. Both classical and modern techniques are presented for strong and weak well-posedness. Propagators seem a natural tool to use due to the structure of the problem, in particular via a duality approach it is possible to obtain estimates using the backward Kolmogorov equation with clear advantages for the needed regularity of the coefficients. We will also notice the difference in the regularization by noise phenomenon in the spatial and measure directions.