Distribution dependent SDEs driven by additive continuous noise

被引：10
|
作者：
Galeati, Lucio [1 ]
Harang, Fabian A. [2 ]
Mayorcas, Avi [3 ]
机构：
[1] Univ Bonn, Inst Appl Math, 53115 Endenicher Allee 60, Bonn, Germany
[2] Univ Oslo, Dept Math, POB 1053,Blindern, N-0316 Oslo, Norway
[3] Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WA, England
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2022年 / 27卷
关键词：
additive noise; pathwise approach; McKean-Vlasov equation; mean field limit; MEAN-FIELD LIMIT; VLASOV EQUATIONS; PROPAGATION; APPROXIMATION; CONVERGENCE; FORCES; CHAOS;
D O I：
10.1214/22-EJP756
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：
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.
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页数：38
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