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

• Main Authors: Liping Xu, Zhi Li, Jiaowan Luo
• Format: Article
• Language: English
• Published: SpringerOpen 2017-05-01
• Series: Advances in Difference Equations
• Subjects: global attracting set; exponential decay in the pth moment; second-order SDEs; fractional Brownian motion
• Online Access: http://link.springer.com/article/10.1186/s13662-017-1186-2

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.