MCKEAN-VLASOV SDE AND SPDE WITH LOCALLY MONOTONE COEFFICIENTS

• 成果类型: Article
• 署名作者: Hong, Wei; Hu, Shanshan; Liu, Wei
• 署名单位: Jiangsu Normal University; University of Bielefeld
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2016
• 发表日期: 2024
• 页码: 2136-2189
• 关键词: distribution dependent sdes; large deviations; well-posedness; differential-equations; granular media; propagation; chaos; uniqueness; EXISTENCE; systems

摘要

In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, that is, locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, the large deviation principle is also derived for the McKean-Vlasov stochastic equations under those weak assumptions. The wide applications of main results are illustrated by various concrete examples such as the granular media equations, plasma -type models, kinetic equations, McKean-Vlasov-type porous media equations and Navier-Stokes equations. In particular, we could remove or relax some typical assumptions previously imposed on those models.