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arXiv · 1702.01397

Smoothing properties of McKean-Vlasov SDEs

Dan Crisan·Eamon McMurray
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Abstract

In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives of the density of the solutions of McKean-Vlasov SDEs.

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Dan Crisan, Eamon McMurray. 2017-02-05. Smoothing properties of McKean-Vlasov SDEs. https://arxiv.org/abs/1702.01397

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