论文标题
HARNACK不平等，用于分配依赖于随机的哈密顿系统
Harnack Inequality for Distribution Dependent Stochastic Hamiltonian System
论文作者
论文摘要
The dimension free Harnack inequality is established for the distribution dependent stochastic Hamiltonian system, where the drift is Lipschitz continuous in the measure variable under the distance induced by the Hölder-Dini continuous functions, which are $β(β>\frac{2}{3})$-Hölder continuous on the degenerate component and square root of Dini continuous on the non-degenerate one.结果扩展了在$ l^2 $ -Wasserstein距离以下的量度变量中，漂移是Lipschitz连续的现有结果。
The dimension free Harnack inequality is established for the distribution dependent stochastic Hamiltonian system, where the drift is Lipschitz continuous in the measure variable under the distance induced by the Hölder-Dini continuous functions, which are $β(β>\frac{2}{3})$-Hölder continuous 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 the measure variable under $L^2$-Wasserstein distance.
