Second order McKean-Vlasov SDEs and kinetic Fokker-Planck-Kolmogorov equations

2021/09/03 by Zhang, Xicheng · 2 citations
#35H10 #60H10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2109.01273

Abstract

In this paper we study second order stochastic differential equations with measurable and density-distribution dependent coefficients. Through establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations with distribution-valued inhomogeneous term, we show the existence of weak solutions under mild assumptions. Moreover, by using the Hölder regularity estimate obtained recently in \citeGIMV19, we also show the well-posedness of generalized martingale problems when diffusion coefficients only depend on the position variable (not necessarily continuous). Even in the non density-distribution dependent case, it seems that this is the first result about the well-posedness of SDEs with measurable diffusion coefficients.

Cited by

• Harnack inequalities for nonlocal operators with supercritical drifts and their applications
• Kinetic SDEs with subcritical distributional drifts

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