Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

被引：66

作者：

Pei, Bin ^{[1
,2
]}

Xu, Yong ^{[3
]}

Wu, Jiang-Lun ^{[4
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Kyushu Univ, Grad Sch Math, Fukuoka, Fukuoka 8190395, Japan

[3] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China

[4] Swansea Univ, Dept Math, Swansea SA1 8EN, W Glam, Wales

来源：

APPLIED MATHEMATICS LETTERS | 2020年 / 100卷

基金：

中国博士后科学基金;

关键词：

Averaging principle; Fractional Brownian motion; Pathwise Riemann-Stieltjes integral; Ito stochastic calculus; DYNAMICAL-SYSTEMS; INEQUALITY; PRINCIPLE;

D O I：

10.1016/j.aml.2019.106006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Ito stochastic calculus to handle both types of integrals involved and proved that the original SDEs can be approximated by averaged SDEs in the manner of mean square convergence. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：8

共 50 条

[1] Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Guerra, Joao
Nualart, David
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2008, 26 (05) : 1053 - 1075
[2] Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Shen, Guangjun
Xiang, Jie
Wu, Jiang-Lun
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 321 : 381 - 414
[3] Reflected stochastic differential equations driven by standard and fractional Brownian motion
Chadad, Monir
Erraoui, Mohamed
[J]. STOCHASTICS AND DYNAMICS, 2024, 24 (02)
[4] Stochastic differential equations driven by fractional Brownian motion
Xu, Liping
Luo, Jiaowan
[J]. STATISTICS & PROBABILITY LETTERS, 2018, 142 : 102 - 108
[5] Averaging Method for Neutral Stochastic Delay Differential Equations Driven by Fractional Brownian Motion
Wang, Peiguang
Xu, Yan
[J]. JOURNAL OF FUNCTION SPACES, 2020, 2020
[6] Neutral stochastic differential equations driven by Brownian motion and fractional Brownian motion in a Hilbert space
Liu, Weiguo
Luo, Jiaowan
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2015, 87 (1-2): : 235 - 253
[7] Averaging Principle for Caputo Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Delays
Duan, Pengju
Li, Hao
Li, Jie
Zhang, Pei
[J]. COMPLEXITY, 2021, 2021
[8] Fuzzy stochastic differential equations driven by fractional Brownian motion
Hossein Jafari
Marek T. Malinowski
M. J. Ebadi
[J]. Advances in Difference Equations, 2021
[9] Approximation of stochastic differential equations driven by fractional Brownian motion
Lisei, Hannelore
Soos, Anna
[J]. SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS V, 2008, 59 : 227 - 241
[10] Fuzzy stochastic differential equations driven by fractional Brownian motion
Jafari, Hossein
Malinowski, Marek T.
Ebadi, M. J.
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)

← 1 2 3 4 5 →