Distribution dependent SDEs driven by fractional Brownian motions

被引：19
|
作者：
Fan, Xiliang [1 ,2 ]
Huang, Xing [3 ]
Suo, Yongqiang [4 ]
Yuan, Chenggui [5 ]
机构：
[1] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China
[2] Univ Bielefeld, Fak Mathemat, D-33615 Bielefeld, Germany
[3] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China
[4] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 211106, Peoples R China
[5] Swansea Univ, Dept Math, Bay campus, Swansea SA1 8EN, Wales
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2022年 / 151卷
基金：
中国国家自然科学基金;
关键词：
Distribution dependent SDE; Fractional Brownian motion; Bismut type formula; Lions derivative; Wasserstein distance; STOCHASTIC DIFFERENTIAL-EQUATIONS; MEAN-FIELD; BISMUT FORMULA; RESPECT; CALCULUS;
D O I：
10.1016/j.spa.2022.05.007
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：
In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H is an element of (0, 1/2)boolean OR(1/2, 1). We prove the well-posedness of this type equations, and then establish a general result on the Bismut formula for the Lions derivative by using Malliavin calculus. As applications, we provide the Bismut formulas of this kind for both non-degenerate and degenerate cases, and obtain the estimates of the Lions derivative and the total variation distance between the laws of two solutions.
引用
收藏
页码：23 / 67
页数：45
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