Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type: the time-dependent case
arXiv:2203.09576 · doi:10.1007/s00028-024-00970-x
Abstract
We consider a large class of nonlinear FPKEs with coefficients of Nemytskii-type depending explicitly on time and space, for which it is known that there exists a sufficiently Sobolev-regular distributional solution u in L^1 and L^\infty. We show that there exists a unique strong solution to the associated McKean-Vlasov SDE with time marginal law densities u. In particular, every weak solution of this equation with time marginal law densities u can be written as a functional of the driving Brownian motion. Moreover, plugging any Brownian motion into this very functional produces a weak solution with time marginal law densities u.
9 pages. arXiv admin note: text overlap with arXiv:2107.07417