McKean-Vlasov SDEs分布的导数估计

arXiv: Probability Pub Date : 2020-06-30 DOI:10.1214/21-EJP582

Xing Huang, Feng-Yu Wang

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引用次数: 8

摘要

通过对冻结SDEs的热核参数展开，估计了Mckean-Vlasov SDEs定律对初始分布的固有导数。作为应用，对于初始分布，两个解之间的总变异距离以Wasserstein距离为界。这些结果推广了最近用耦合方法和Malliavin演算对无分布噪声所证明的一些结果。

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Derivative estimates on distributions of McKean-Vlasov SDEs

By using the heat kernel parameter expansion with respect to the frozen SDEs, the intrinsic derivative is estimated for the law of Mckean-Vlasov SDEs with respect to the initial distribution. As an application, the total variation distance between the laws of two solutions is bounded by the Wasserstein distance for initial distributions. These extend some recent results proved for distribution-free noise by using the coupling method and Malliavin calculus.

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arXiv: Probability

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