Optimal index and averaging principle for Ito-Doob stochastic fractional differential equations

被引：8

作者：

Wang, Wenya ^{[1
]}

Guo, Zhongkai ^{[2
]}

机构：

[1] Jianghan Univ, Sch Artificial Intelligence, Wuhan 430056, Peoples R China

[2] South Cent Univ, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2022年 / 22卷 / 06期

关键词：

Optimal index; Ito-Doob SFDEs; Averaging principle;

D O I：

10.1142/S0219493722500186

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, a class of Ito-Doob stochastic fractional differential equations (Ito-Doob SFDEs) models are discussed. Using the time scale transformation method, we consider the averaging principle of the transformed equations and establish the relevant results. At the same time, we find that the optimal index for the original Ito-Doob SFDEs can be determined, the selection of such index is similar to the classical stochastic differential equations model.

引用

页数：14

共 12 条

[1]

Duan J., 2014, Effective Dynamics of Stochastic Partial Differential Equations

[2] AN AVERAGING PRINCIPLE FOR TWO-SCALE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS [J].

Fu, Hongbo ;

Duan, Jinqiao .

STOCHASTICS AND DYNAMICS, 2011, 11 (2-3) :353-367

[3] Averaging principle for stochastic Korteweg-de Vries equation [J].

Gao, Peng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (12) :6872-6909

[4] Averaging principle for stochastic differential equations under a weak condition [J].

Guo, Zhongkai ;

Lv, Guangying ;

Wei, Jinlong .

CHAOS, 2020, 30 (12)

[5] On the representation of fractional Brownian motion as an integral with respect to (dt)a [J].

Jumarie, G .

APPLIED MATHEMATICS LETTERS, 2005, 18 (07) :739-748

[6]

Kilbas A.A., 2006, THEORY APPL FRACTION, DOI DOI 10.1016/S0304-0208(06)80001-0

[7]

Mahmoud A., 2019, STOCH DYNAM, V19

[8] Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion [J].

Pei, Bin ;

Xu, Yong ;

Wu, Jiang-Lun .

APPLIED MATHEMATICS LETTERS, 2020, 100

[9] Average and deviation for slow-fast stochastic partial differential equations [J].

Wang, W. ;

Roberts, A. J. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (05) :1265-1286

[10] An Averaging Principle for Multivalued Stochastic Differential Equations [J].

Xu, Jie ;

Liu, Jicheng .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2014, 32 (06) :962-974

← 1 2 →