Global attractiveness and exponential decay of neutral stochastic functional differential equations driven by fBm with Hurst parameter less than 1/2

doi:10.1007/s11464-018-0728-6

Front. Math. China

2018, Vol. 13

Issue (6) : 1469-1487 https://doi.org/10.1007/s11464-018-0728-6

RESEARCH ARTICLE

Global attractiveness and exponential decay of neutral stochastic functional differential equations driven by fBm with Hurst parameter less than 1/2

Liping XU¹(

), Jiaowan LUO²

¹. School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
². School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

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Abstract

We are concerned with a class of neutral stochastic functional differential equations driven by fractional Brownian motion (fBm) in the Hilbert space. We obtain the global attracting sets of this kind of equations driven by fBm with Hurst parameter $ℏ ∈$ (0, 1/2): Especially, some suffcient conditions which ensure the exponential decay in the p-th moment of the mild solution of the considered equations are obtained. In the end, one example is given to illustrate the feasibility and effectiveness of results obtained.

Keywords Global attracting sets exponential p-th moment stability fractional Brownian motion (fBm)

Corresponding Author(s): Liping XU

Issue Date: 02 January 2019

Cite this article:

Liping XU,Jiaowan LUO. Global attractiveness and exponential decay of neutral stochastic functional differential equations driven by fBm with Hurst parameter less than 1/2[J]. Front. Math. China, 2018, 13(6): 1469-1487.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0728-6
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I6/1469

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