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

被引：79

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 18 条

[1]

Decreusefond L., 1998, ESAIM P, V5, P75

[2] Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion [J].

Guerra, Joao ;

Nualart, David .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2008, 26 (05) :1053-1075

[3] Stochastic averaging principles for multi-valued stochastic differential equations driven by poisson point Processes [J].

Guo, Rong ;

Pei, Bin .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2018, 36 (04) :751-766

[4] A LIMIT THEOREM FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH RANDOM RIGHT-HAND SIDES [J].

KHASMINSKII, RZ .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1966, 11 (03) :390-+

[5]

Kolmogoroff AN, 1940, CR ACAD SCI URSS, V26, P115

[6] The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type [J].

Kubilius, K .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 98 (02) :289-315

[7]

Lyons T, 1994, MATH RES LETT, V1, P451

[8] FRACTIONAL BROWNIAN MOTIONS FRACTIONAL NOISES AND APPLICATIONS [J].

MANDELBROT, BB ;

VANNESS, JW .

SIAM REVIEW, 1968, 10 (04) :422-+

[9]

Mishura Y. S., 2008, Lecture Notes in Math

[10]

Nualart D., 2002, Collect. Math., V53, P55

← 1 2 →