Global attracting set and exponential decay of second-order neutral stochastic functional differential equations driven by fBm

Advances in Difference Equations

Zhi Li¹  Jiaowan Luo²  Liping Xu² 

[1] School of Information and Mathematics, Yangtze University;School of Mathematics and Information Sciences, Guangzhou University;

关键词: global attracting set;    exponential decay in the pth moment;    second-order SDEs;    fractional Brownian motion;   

DOI  :  10.1186/s13662-017-1186-2

来源: DOAJ

【 摘 要 】

Abstract In this paper, we are concerned with a class of second-order neutral stochastic functional differential equations driven by a fractional Brownian motion with Hurst parameter 1 / 2 < ħ < 1 $1/2<\hbar <1$ on the Hilbert space. By combining some stochastic analysis theory and new integral inequality techniques, we identify the global attracting sets of the equations under investigation. Some sufficient conditions ensuring the exponential decay of mild solutions in the pth moment to the stochastic systems are obtained. Last, an example is presented to illustrate our theory in the work.

【 授权许可】

Unknown