Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion
Year: 2022
Author: Yarong Peng, Zhi Li, Liping Xu
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 4 : pp. 414–440
Abstract
In this paper, we are concerned with a class of impulsive neutral stochastic functional different equations driven by tempered fractional Brownian motion in the Hilbert space. We obtain the global attracting and quasi-invariant sets of the considered equations driven by tempered fractional Brownian motion $B^{α,λ}(t)$ with $0<α<1/2$ and $λ>0.$ In particular, we give some sufficient conditions which ensure the exponential decay in the $p$-th moment of the mild solution of the considered equations. Finally, an example is given to illustrate the feasibility and effectiveness of the results obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2021-0082
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 4 : pp. 414–440
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Global attracting set quasi-invariant sets tempered fractional Brownian motion exponential decay.