Impulsive stochastic fractional differential equations driven by fractional Brownian motion

Advances in Difference Equations

article

Abouagwa, Mahmoud¹  Cheng, Feifei²  Li, Ji² 

[1] Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University;School of Mathematics and Statistics, Huazhong University of Science and Technology

关键词: Impulsive stochastic differential equations;    Existence and uniqueness;    Fractional calculus;    Fractional Brownian motion;   

DOI  :  10.1186/s13662-020-2533-2

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this research, we study the existence and uniqueness results for a new class of stochastic fractional differential equations with impulses driven by a standard Brownian motion and an independent fractional Brownian motion with Hurst index $1/2< H<1$ under a non-Lipschitz condition with the Lipschitz one as a particular case. Our analysis depends on an approximation scheme of Carathéodory type. Some previous results are improved and extended.

【 授权许可】

CC BY