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 - <p style="text-align: justify;">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 $0&lt;α&lt;1/2$ and $λ&gt;0.$ 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.</p>