2019
DOI: 10.3934/dcdsb.2018272
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Long time behavior of fractional impulsive stochastic differential equations with infinite delay

Abstract: This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive stochastic differential equations with infinite delay driven by both K-valued Q-cylindrical Brownian motion and fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). A general framework which provides an effective way to prove the continuous dependence of mild solutions on initial value is established under some appropriate assumptions. Furthermore, it is also proved the exponential decay… Show more

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Cited by 14 publications
(24 citation statements)
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“…Although the content of this section can be found in several published works (see, e.g. [28]), we prefer to include it in our paper to make it more readable and as much as self-contained as possible.…”
Section: Preliminariesmentioning
confidence: 99%
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“…Although the content of this section can be found in several published works (see, e.g. [28]), we prefer to include it in our paper to make it more readable and as much as self-contained as possible.…”
Section: Preliminariesmentioning
confidence: 99%
“…Xu and Caraballo analyzed in [28] these previously mentioned issues for the following impulsive fractional stochastic delay differential equation (see [28] for the details on the operators and noise)…”
Section: Introductionmentioning
confidence: 99%
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