MULTIVALUED STOCHASTIC MCKEAN-VLASOV EQUATION

被引：5
作者：
Chi, Hongmei [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2014年 / 34卷 / 06期
基金：
中国国家自然科学基金;
关键词：
multivalued SDE; McKean-Vlasov system; maximal monotone operator; DIFFERENTIAL-EQUATIONS; PROBABILISTIC APPROACH; SKOROHOD PROBLEM;
D O I：
10.1016/S0252-9602(14)60118-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McKean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.
引用
收藏
页码：1731 / 1740
页数：10
相关论文
共 16 条
[1]  
[Anonymous], 2001, Foundations of Modern Probability
[2]  
[Anonymous], OPERATEURS MONOTONES
[3]   Probabilistic approach for granular media equations in the non-uniformly convex case [J].
Cattiaux, P. ;
Guillin, A. ;
Malrieu, F. .
PROBABILITY THEORY AND RELATED FIELDS, 2008, 140 (1-2) :19-40
[4]   Diffusing particles with electrostatic repulsion [J].
Cepa, E ;
Lepingle, D .
PROBABILITY THEORY AND RELATED FIELDS, 1997, 107 (04) :429-449
[5]   Multivalued Skorohod problem [J].
Cepa, E .
ANNALS OF PROBABILITY, 1998, 26 (02) :500-532
[6]  
Cepa E., 1995, LECT NOTES MATH, V1613, P86, DOI DOI 10.1007/BFB0094202
[7]   MCKEAN-VLASOV ITO-SKOROHOD EQUATIONS, AND NONLINEAR DIFFUSIONS WITH DISCRETE JUMP SETS [J].
GRAHAM, C .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1992, 40 (01) :69-82
[8]   Solving Landau equation for some soft potentials through a probabilistic approach [J].
Guérin, H .
ANNALS OF APPLIED PROBABILITY, 2003, 13 (02) :515-539
[9]  
Hu YZ, 2010, ACTA MATH SCI, V30, P2033
[10]  
Meleard S, 1996, LECT NOTES MATH, V1627, P42
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