Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 6: 1469 - 1487

DOI: 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 XU , 1 ,
  • Jiaowan LUO 2
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  • 1. School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
  • 2. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Received date: 01 Mar 2018

Accepted date: 03 Sep 2018

Published date: 02 Jan 2019

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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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.

Key words： Global attracting sets; exponential p-th moment stability; fractional Brownian motion (fBm)

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]. Frontiers of Mathematics in China, 2018 , 13(6) : 1469 -1487 . DOI: 10.1007/s11464-018-0728-6

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