Stability of the nonlinear stochastic process that approximates the system of interacting Brownian particles

被引：1
|
作者：
Yarykin, P. N. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Chair Probabil Theory, Dept Mech & Math, Moscow 119992, Russia
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2007年 / 51卷 / 02期
关键词：
nonlinear stochastic process; McKean-Vlasov equation; stability;
D O I：
10.1137/S0040585X97982372
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The nonlinear SEE of McKean-Vlasov type in the absence of external fields is considered. First; the existence and the uniqueness of the equation solution are proved. Next, the existence and the uniqueness of the stationary solution at the class of probability with fixed expectation are proved. Also; weak convergence to invariant probability is proved.
引用
收藏
页码：387 / 396
页数：10
相关论文
共 50 条
  • [41] Stochastic bifurcation and nonlinear dynamics analysis of stochastic wheelset system with double time delays
    Zhang, Jiangang
    Wang, Xinyang
    He, Meijuan
    An, Xinlei
    Wei, Lixiang
    PROBABILISTIC ENGINEERING MECHANICS, 2025, 80
  • [42] New approach of stability switched nonlinear system
    Hamidi, Faical
    Abdelkrim, Mohamed Naceur
    Aggoune, Woihiba
    3RD INTERNATIONAL CONFERENCE ON CONTROL, ENGINEERING & INFORMATION TECHNOLOGY (CEIT 2015), 2015,
  • [43] Stability Analysis of Switched Stochastic Nonlinear Systems With State-Dependent Delay
    Fan, Lina
    Zhu, Quanxin
    Zheng, Wei Xing
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2024, 69 (04) : 2567 - 2574
  • [44] Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects
    Li, Chunxiang
    Sun, Jitao
    Sun, Ruoyan
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2010, 347 (07): : 1186 - 1198
  • [45] The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations
    Song, Guoting
    Hu, Junhao
    Gao, Shuaibin
    Li, Xiaoyue
    NUMERICAL ALGORITHMS, 2022, 89 (02) : 855 - 883
  • [46] Advances in nonlinear hybrid stochastic differential delay equations: Existence, boundedness and stability
    Hu, Junhao
    Mao, Wei
    Mao, Xuerong
    AUTOMATICA, 2023, 147
  • [47] Stability analysis of nonlinear stochastic differential delay systems under impulsive control
    Li, Chunxiang
    Sun, Jitao
    PHYSICS LETTERS A, 2010, 374 (09) : 1154 - 1158
  • [48] Stability of a Class of Nonlinear Neutral Stochastic Differential Equations with Variable Time Delays
    Wu, Meng
    Huang, Nanjing
    Zhao, Changwen
    ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2012, 20 (01): : 467 - 487
  • [49] The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations
    Guoting Song
    Junhao Hu
    Shuaibin Gao
    Xiaoyue Li
    Numerical Algorithms, 2022, 89 : 855 - 883
  • [50] Stability and Stabilization of Nonlinear Stochastic Systems With Synchronous and Asynchronous Switching Parameters to the States
    Liu, Linna
    Deng, Feiqi
    IEEE TRANSACTIONS ON CYBERNETICS, 2023, 53 (08) : 4894 - 4907
12345