Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process

doi:10.1007/s11464-017-0672-x

Front. Math. China

2018, Vol. 13

Issue (1) : 87-105 https://doi.org/10.1007/s11464-017-0672-x

RESEARCH ARTICLE

Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process

Zhi LI^1,², Litan YAN¹(

), Xianghui ZHOU²

¹. College of Information Science and Technology, Donghua University, Shanghai 201620, China
². School of Information and Mathematics, Yangtze University, Jingzhou 434023, China

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Abstract

We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and stochastic integral inequalities, we identify the global attracting sets of this kind of equations. Especially, some sufficient conditions ensuring the exponent p-stability of mild solutions to the stochastic systems under investigation are obtained. Last, an example is given to illustrate the theory in the work.

Keywords Global attracting sets exponential p-th moment stability Rosenblatt process

Corresponding Author(s): Litan YAN

Issue Date: 12 January 2018

Cite this article:

Zhi LI,Litan YAN,Xianghui ZHOU. Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process[J]. Front. Math. China, 2018, 13(1): 87-105.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0672-x
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I1/87

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