Volume 38, Issue 4
Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion

Yarong Peng, Zhi Li & Liping Xu

Ann. Appl. Math., 38 (2022), pp. 414-440.

Published online: 2022-11

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  • 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.

  • AMS Subject Headings

60H15

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COPYRIGHT: © Global Science Press

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@Article{AAM-38-414, author = {Peng , YarongLi , Zhi and Xu , Liping}, title = {Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {38}, number = {4}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2021-0082}, url = {http://global-sci.org/intro/article_detail/aam/21165.html} }
TY - JOUR T1 - Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion AU - Peng , Yarong AU - Li , Zhi AU - Xu , Liping JO - Annals of Applied Mathematics VL - 4 SP - 414 EP - 440 PY - 2022 DA - 2022/11 SN - 38 DO - http://doi.org/10.4208/aam.OA-2021-0082 UR - https://global-sci.org/intro/article_detail/aam/21165.html KW - Global attracting set, quasi-invariant sets, tempered fractional Brownian motion, exponential decay. AB -

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.

Yarong Peng, Zhi Li & Liping Xu. (2022). Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion. Annals of Applied Mathematics. 38 (4). 414-440. doi:10.4208/aam.OA-2021-0082
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