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arXiv · 2203.09576

Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type: the time-dependent case

Sebastian Grube
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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.

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Sebastian Grube. 2022-03-17. Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type: the time-dependent case. https://doi.org/10.1007/s00028-024-00970-x

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