Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion

被引：0
作者：
Chen Fei
Wei-yin Fei
Li-tan Yan
机构：
[1] Donghua University,Glorious Sun School of Business and Management
[2] Anhui Polytechnic University,School of Mathematics and Physics
来源：
Applied Mathematics-A Journal of Chinese Universities | 2019年 / 34卷
关键词：
stochastic differential delay equation (SDDE); sublinear expectation; existence and uniqueness; -Brownian motion; stability and boundedness; 60H10; 93E15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper, by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.
引用
收藏
页码：184 / 204
页数：20
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