Stochastic averaging principle for neutral stochastic functional differential equations driven by G-Levy process

被引：0

作者：

Shen, Guangjun ^{[1
]}

Fan, Jingjing ^{[1
]}

Wu, Jiang-Lun ^{[2
,3
]}

Wang, Zhi ^{[4
]}

机构：

[1] Anhui Normal Univ, Dept Math, Wuhu 241000, Peoples R China

[2] BNU HKBU United Int Coll, Fac Sci & Technol, Dept Math Sci, Zhuhai 519087, Peoples R China

[3] UIC, Guangdong Prov Key Lab Interdisciplinary Res & App, Zhuhai 519087, Peoples R China

[4] Ningbo Univ Technol, Sch Stat & Data Sci, Ningbo 315211, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2024年 / 24卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Averaging principle; stochastic functional differential equation; G-Levy process; mean square convergence; G-BROWNIAN MOTION; REPRESENTATION THEOREM; CALCULUS; EXPECTATION; STABILITY;

D O I：

10.1142/S0219493724500291

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 aim to establish an averaging principle for neutral stochastic functional differential equations driven by G-Levy processes with non-Lipschitz coefficients. Utilizing the theory of sub-linear expectations, we show that the solutions of the considered stochastic systems can be approximated by the solutions of averaged neutral stochastic functional differential equations driven by G-Levy processes in the mean square convergence and convergence in the sense of capacity. Finally, we give an example to support our main results.

引用

页数：25

共 36 条

[21]

Peng S, 2007, ABEL SYMP, V2, P541

[22] Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations [J].

Peng ShiGe .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (07) :1391-1411

[23] Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation [J].

Peng, Shige .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2008, 118 (12) :2223-2253

[24]

Qiao H., 2020, ARXIV

[25] On representation theorem of sublinear expectation related to G-Levy process and paths of G-Levy process [J].

Ren, Liying .

STATISTICS & PROBABILITY LETTERS, 2013, 83 (05) :1301-1310

[26] Path independence of additive functionals for stochastic differential equations under G-framework [J].

Ren, Panpan ;

Yang, Fen-Fen .

FRONTIERS OF MATHEMATICS IN CHINA, 2019, 14 (01) :135-148

[27] STABILIZATION OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY G-LEVY PROCESS WITH DISCRETE-TIME FEEDBACK CONTROL [J].

Shen, Guangjun ;

Wu, Xueying ;

Yin, Xiuwei .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021, 26 (02) :755-774

[28] Averaging principle for fractional heat equations driven by stochastic measures [J].

Shen, Guangjun ;

Wu, Jiang-Lun ;

Yin, Xiuwei .

APPLIED MATHEMATICS LETTERS, 2020, 106

[29] Martingale representation theorem for the G-expectation [J].

Soner, H. Mete ;

Touzi, Nizar ;

Zhang, Jianfeng .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2011, 121 (02) :265-287

[30]

Wang B., 2017, ADV DIFFER EQU-NY, V188, P1

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