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

页码：23 / 67

页数：45

共 50 条

[21] Stochastic Averaging Principle for Two-Time-Scale SDEs with Distribution-Dependent Coefficients Driven by Fractional Brownian Motion
Shen, Guangjun
Yin, Jiayuan
Wu, Jiang-Lun
COMMUNICATIONS IN MATHEMATICS AND STATISTICS, 2023,
[22] SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS
Han, Yuecai
Sun, Yifang
ACTA MATHEMATICA SCIENTIA, 2018, 38 (02) : 681 - 694
[23] SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS
韩月才
孙一芳
Acta Mathematica Scientia(English Series), 2018, 38 (02) : 681 - 694
[24] HARNACK INEQUALITIES FOR FUNCTIONAL SDES DRIVEN BY SUBORDINATE FRACTIONAL BROWNIAN MOTION
LI, Z. H. I.
Peng, Y. A. R. O. N. G.
Yan, L. I. T. A. N.
JOURNAL OF MATHEMATICAL INEQUALITIES, 2022, 16 (04): : 1429 - 1453
[25] Harnack inequalities for McKean-Vlasov SDEs driven by subordinate Brownian motions
Deng, Chang-Song
Huang, Xing
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 519 (01)
[26] Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion
Li, Zhi
Luo, Jiaowan
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2014, 22 (04) : 213 - 226
[27] Stochastic differential equations driven by fractional Brownian motions
Jien, Yu-Juan
Ma, Jin
BERNOULLI, 2009, 15 (03) : 846 - 870
[28] Solutions to BSDEs Driven by Multidimensional Fractional Brownian Motions
Miao, Jie
Yang, Xu
MATHEMATICAL PROBLEMS IN ENGINEERING, 2015, 2015
[29] On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion
Nourdin, I
Simon, T
STATISTICS & PROBABILITY LETTERS, 2006, 76 (09) : 907 - 912
[30] Harnack Type Inequalities for SDEs Driven by Fractional Brownian Motion with Markovian Switching
Pei, Wenyi
Yan, Litan
Chen, Zhenlong
ACTA MATHEMATICA SCIENTIA, 2023, 43 (03) : 1403 - 1414

← 1 2 3 4 5 →