分布相关二阶随机微分方程的哈纳克不等式

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-06-18 DOI:10.1007/s10959-024-01346-0

Xing Huang, Xiaochen Ma

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引用次数: 0

摘要

通过研究与分布相关的二阶随机微分方程相关的非线性半群 \(P_t^*\)的正则性，得出了当漂移在度量变量中为 Lipschitz 连续时的哈纳克不等式，该不等式是由\(\beta \)-Hölder连续（在退化分量上为\(\beta > \frac{2}{3}\），在非退化分量上为 Dini 的平方根连续的函数所引起的距离下的。这些结果扩展了现有结果，其中漂移在 \(L^2\)-Wasserstein 距离上是 Lipschitz 连续的。

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Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations

By investigating the regularity of the nonlinear semigroup \(P_t^*\) associated with the distribution dependent second-order stochastic differential equations, the Harnack inequality is derived when the drift is Lipschitz continuous in the measure variable under the distance induced by the functions being \(\beta \)-Hölder continuous (with \(\beta > \frac{2}{3}\)) on the degenerate component and square root of Dini continuous on the non-degenerate one. The results extend the existing ones in which the drift is Lipschitz continuous in \(L^2\)-Wasserstein distance.

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.