Stabilities of delay stochastic McKean-Vlasov equations in the G-framework  

作　　者：Haiyan YUAN Quanxin ZHU 

机构地区：[1]Department of Mathematics,Heilongjiang Institute of Technology,Harbin 150050,China [2]Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education),School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,China

出　　处：《Science China(Information Sciences)》2025年第1期252-274,共23页中国科学(信息科学)(英文版)

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12271368,62173139);Natural Science Foundation of Hunan Province(Grant No.2023JJ30388);Science and Technology Innovation Program of Hunan Province(Grant No.2021RC4030);Natural Science Foundation of Heilongjiang Province(Grant No.LH2023A019);Foundation of Innovation Talent of Heilongjiang Institute of Technology(Grant Nos.2024GJ01,2023GJ10).

摘　　要：This article focuses on a type of stochastic McKean-Vlasov equation in the G-framework(G-SMVE)and addresses the stability issue for delay stochastic McKean-Vlasov equations in the G-framework(G-SMVDEs).Distribution dependence and uncertainty prevent us from directly applying the stochastic analysis method for stochastic McKean-Vlasov equations(SMVEs)to G-SMVEs directly.To overcome this difficulty,we introduce definitions,including the derivative of a function with a law under the G-expectation and the Lions derivatives.Then we construct a new G-Itô formula for G-SMVEs according to the G-Itô formula for stochastic differential equations in the G-framework(G-SDEs)and the Itô formula for SMVEs.Using the new G-Itô formula and the Lyapunov functional method,we investigate the moment exponential stability and almost sure asymptotic stability of G-SMVDEs.To overcome the difficulty in obtaining the distribution dependence of the exact solution to the G-SMVDE,we introduce the empirical measure and the corresponding interacting particle system,and then prove the stability equivalence between the underlying G-SMVDE and the corresponding interacting particle system.Two examples are used to confirm our theoretical results.

关 键 词：delay stochastic McKean-Vlasov equations Wasserstein distance G-Brownian motion Lions derivative stability 

分 类 号：O211.63[理学—概率论与数理统计]