Global attracting set and exponential decay of coupled neutral SPDEs driven by fractional Brownian motion. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Li, Zhi; Xu, Liping; Yan, Litan
• Is Part Of: Stochastics. Volume 93:Issue 1(2021)
• Page Start: 3
• Page End: 28
• Publication Date: 2021-01-02
• Subjects: Global attracting set -- exponential decay in the pth moment -- coupled systems -- fractional Brownian motion; 60H15 -- 60G15 -- 60H05; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1697270
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : In this paper, we are concerned with a class of coupled neutral stochastic partial differential equations driven by fractional Brownian motion with Hurst parameter H ∈ ( 0, 1 / 2 ) ∪ ( 1 / 2, 1 ) . On account of the Perov's fixed point theorem and semigroup theory, we prove the existence and uniqueness of mild solution. Subsequently, by using delay integral inequalities, we identify the global attracting sets of the equations under investigation. Furthermore, we obtain some sufficient conditions that ensure the exponential decay of mild solutions in the p th moment. Lastly, we present an example to illustrate our theory in this work.