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arXiv · 2101.04080

Nonlinear McKean-Vlasov diffusions under the weak Hormander condition with quantile-dependent coefficients

Yaozhong Hu·Michael A. Kouritzin·Jiayu Zheng
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Abstract

In this paper, the strong existence and uniqueness for a degenerate finite system of quantile-dependent McKean-Vlasov stochastic differential equations are obtained under a weak H\"{o}rmander condition. The approach relies on the apriori bounds for the density of the solution to time inhomogeneous diffusions. The time inhomogeneous Feynman-Fac formula is used to construct a contraction map for this degenerate system.

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Yaozhong Hu, Michael A. Kouritzin, Jiayu Zheng. 2021-01-11. Nonlinear McKean-Vlasov diffusions under the weak Hormander condition with quantile-dependent coefficients. https://arxiv.org/abs/2101.04080

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