Exponential Ergodicity and Propagation of Chaos for Path-Distribution Dependent Stochastic Hamiltonian System
Probability
2023-03-29 v4
Abstract
By Girsanov's thoerem and using the existing log-Harnack inequality for distribution independent SDEs, the log-Harnack inequality is derived for path-distribution dependent stochastic Hamiltonian systems. 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, which together with the coupling by change of measure implies the quantitative propagation of chaos in total variation norm as well as relative entropy are obtained.
Keywords
Cite
@article{arxiv.2109.13728,
title = {Exponential Ergodicity and Propagation of Chaos for Path-Distribution Dependent Stochastic Hamiltonian System},
author = {Xing Huang and Wujun Lv},
journal= {arXiv preprint arXiv:2109.13728},
year = {2023}
}
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23 pages