路径-分布相关随机哈密顿系统的指数遍历性与混沌的传播

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2023-01-01 DOI:10.1214/23-ejp1027

Xing Huang, Wujun Lv

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引用次数: 2

摘要

根据Girsanov定理，利用分布无关SDEs的log-Harnack不等式，导出了路径-分布相关随机哈密顿系统的log-Harnack不等式。作为应用，结合运输成本不等式，得到了相对熵的指数遍历性。此外，得到了混沌在Wasserstein距离意义上的定量传播，并结合测度变化耦合，得到了混沌在总变范数和相对熵上的定量传播。

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Exponential ergodicity and propagation of chaos for path-distribution dependent stochastic Hamiltonian system

By Girsanov’s theorem and using the existing log-Harnack inequality for distribution independent SDEs, the log-Harnack inequality is derived for path-distribution dependent stochastic Hamiltonian system. As an application, the exponential ergodicity in relative entropy is obtained by combining with transportation cost inequality. In addition, the quantitative propagation of chaos in the sense of Wasserstein distance is obtained, which together with the coupling by change of measure implies the quantitative propagation of chaos in total variation norm as well as relative entropy.

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来源期刊

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

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.