Delay-dependent Asymptotic Stability of Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion

被引：26

作者：

Fei, Chen ^{[1
]}

Fei, Weiyin ^{[2
,3
]}

Mao, Xuerong ^{[4
]}

Yan, Litan ^{[5
]}

机构：

[1] Univ Shanghai Sci & Technol, Business Sch, Shanghai 200093, Peoples R China

[2] Anhui Polytech Univ, Key Lab Adv Percept & Intelligent Control High En, Minist Educ, Wuhu 241000, Peoples R China

[3] Anhui Polytech Univ, Sch Math Phys & Finance, Wuhu 241000, Peoples R China

[4] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[5] Donghua Univ, Coll Sci, Dept Stat, Shanghai 201620, Peoples R China

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2022年 / 359卷 / 09期

基金：

中国国家自然科学基金;

关键词：

REPRESENTATION THEOREM; AMBIGUOUS VOLATILITY; PORTFOLIO CHOICE; FEEDBACK-CONTROL; BOUNDEDNESS; CALCULUS; SYSTEMS; STABILIZATION; EXPECTATIONS; UTILITY;

D O I：

10.1016/j.jfranklin.2022.03.027

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Based on the classical probability, the stability of stochastic differential delay equations (SDDEs) whose coefficients are growing at most linearly has been investigated intensively. Moreover, the delay-dependent stability of highly nonlinear hybrid stochastic differential equations (SDEs) has also been studied recently. In this paper, using the nonlinear expectation theory, we first explore the delay-dependent criteria on the asymptotic stability for a class of highly nonlinear SDDEs driven by G-Brownian motion (G-SDDEs). Then, the (weak) quasi-sure stability of solutions to G-SDDEs is developed. Finally, an example is analyzed by the phi-max-mean algorithm to illustrate our theoretical results. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

引用

页码：4366 / 4392

页数：27

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