Weak Solution and Invariant Probability Measure for McKean-Vlasov SDEs with Integrable Drifts
Probability
2021-10-19 v4
Abstract
In this paper, by utilizing Wang's Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for McKean-Vlasov SDEs with integrable drift is investigated. In addition, using the decoupled method, some regularity such as relative entropy and Sobolev's estimate of invariant probability measure are proved. Finally, by Banach's fixed theorem, the existence and uniqueness of invariant probability measure for symmetric McKean-Vlasov SDEs and stochastic Hamiltonian system with integrable drifts are obtained.
Keywords
Cite
@article{arxiv.2108.05802,
title = {Weak Solution and Invariant Probability Measure for McKean-Vlasov SDEs with Integrable Drifts},
author = {Xing Huang and Shen Wang and Fen-Fen Yang},
journal= {arXiv preprint arXiv:2108.05802},
year = {2021}
}
Comments
15 pages