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Nonlinear McKean-Vlasov Diffusions under the Weak Hörmander Condition with Quantile-Dependent Coefficients

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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 Hörmander condition. The approach relies on the a priori 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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Funding

The authors are supported by NSERC discovery grants and a centennial fund from University of Alberta at Edmonton; National Natural Science Foundation of China grant (Grant No. 11901598). Data sharing not applicable to this article as no datasets were generated or analysed during the current study

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Yaozhong Hu & Michael A. Kouritzin

  2. Faculty of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, Shenzhen, 518172, China

    Jiayu Zheng

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  1. Yaozhong Hu
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  2. Michael A. Kouritzin
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  3. Jiayu Zheng
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Correspondence to Jiayu Zheng.

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Hu, Y., Kouritzin, M.A. & Zheng, J. Nonlinear McKean-Vlasov Diffusions under the Weak Hörmander Condition with Quantile-Dependent Coefficients. Potential Anal 60, 1093–1119 (2024). https://doi.org/10.1007/s11118-023-10080-x

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