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Sensitivity to small delays of mean square stability for stochastic neutral evolution equations

  • *Corresponding author

    *Corresponding author 

Dedicated to Professor Tomás Caraballo on occasion of his 60th Birthday

Wei Wang is supported by China Scholarship Council (Grant No. 201708120038) and National Natural Science Foundation of China (Grant No. 11601382). Kai Liu is supported by Tianjin Thousand Talents Plan and Xiulian Wang is supported by Project of Tianjin Municipal Education Commission (Grant No. JW1714)

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  • In this work, we are concerned about the mean square exponential stability property for a class of stochastic neutral functional differential equations with small delay parameters. Both distributed and point delays under the neutral term are considered. Sufficient conditions are given to capture the exponential stability in mean square of the stochastic system under consideration. As an illustration, we present some practical systems to show their exponential stability which is not sensitive to small delays in the mean square sense.

    Mathematics Subject Classification: Primary: 60H15, 60G15; Secondary: 60H05.

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    [7] K. LiuStochastic Stability of Differential Equations in Abstract Spaces, Cambridge University Press, 2019.  doi: 10.1017/9781108653039.
    [8] K. Liu, Stationary solutions of neutral stochastic partial differential equations with delays in the highest-order derivatives, Discrete Cont. Dyn. Sys.-B, 23 (2018), 3915-3934. 
    [9] H. Tanabe, Equations of Evolution, Pitman, New York, 1979.
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