Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion

Advances in Difference Equations

Yong Ren¹  Pengju Duan² 

[1] Department of Mathematics, Anhui Normal University, Wuhu, China;School of Mathematics and Statistics, Suzhou University, Anhui, China

关键词: impulsive integral inequality;    fractional Brownian motion;    attracting set;    quasi-invariant set;    stochastic integro-differential equation;    60H15;    35B35;    39B82;    93E03;   

DOI  :  10.1186/s13662-017-1411-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The paper is devoted to investigating a class of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion. By establishing two new impulsive integral inequalities which improve the inequalities established by Li (Neurocomputing 177:620-627, 2016) and Long et al. (Stat. Probab. Lett. 82(9):1699-1709, 2012), attracting and quasi-invariant sets of the system are obtained. Moreover, exponential stability of the mild solution is established with sufficient conditions.

【 授权许可】

CC BY