Journal of Guangdong University of Technology ›› 2020, Vol. 37 ›› Issue (06): 56-62.doi: 10.12052/gdutxb.190160

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Stability of Solutions for a Class of Impulsive Stochastic Differential Equations

Huang Hui-min, Guo Cheng-jun   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2019-12-19 Online:2020-11-02 Published:2020-11-02

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Abstract: The stability of solutions of a class of impulsive stochastic differential equations was studied by using the fixed point theory and Lyapunov stability theorem and sufficient conditions for the exponential stability in the mean square of the equation are obtained.

Key words: fixed point theory, Lyapunov functional, impulsive, stability

CLC Number: 

  • O175
[1] LIU K. Stability of infinite dimensional stochastic differential equations with applications[M]. London: Chapman & Hall/CRC, 2005.
[2] MAO X R. Exponential stability in mean square of neutral stochastic differential functional equations [J]. Systems and Control Letters, 1995, 26(4): 245-251.
[3] GUO C J, O’REGAN D, DENG F Q. Fixed points and exponential stability for a stochastic neutral cellular network [J]. Applied Mathematics Letters, 2013, 26(8): 849-853.
[4] LI D S, FAN X M. Exponential stability of impulsive stochastic partial differential equations with delays [J]. Statistics and Probability Letters, 2017, 126: 185-192.
[5] HU W, ZHU Q X. Moment exponential stability of stochastic nonlinear delay systems with impulse effects at random times [J]. International Journal of Robust and Nonlinear Control, 2009, 29: 3809-3820.
[6] FU X Z, ZHU Q X, GUO Y X. Stabilization of stochastic functional differential systems with delayed impulses [J]. Applied Mathematics and Computation, 2019, 346: 776-789.
[7] YU G S, YANG W Q, XU L. Pth moment and almost sure exponential stability of impulsive neutral stochastic functional differential equations with markovian switching [J]. International Journal of Systems Science, 2018, 49(6): 1164-1177.
[8] LUO J W. Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays [J]. Journal of Mathematical Analysis and Applications, 2008, 342(2): 753-760.
[9] 徐林, 宋常修. 一类三阶时滞微分方程的稳定性和有界性[J]. 广东工业大学学报, 2015, 32(1): 128-132.
XU L, SONG C X. Stability and boundedness of a class of third-order delay differential equations [J]. Journal of Guangdong University of Technology, 2015, 32(1): 128-132.
[10] CHENGUP, DENG F Q. Global exponential stability of impulsive stochastic functional Differential systems [J]. Statistics and Probability Letters, 2010, 80(23-24): 1854-1862.
[11] CHENGUP, DENGUF Q, YAOUF Q. Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects [J]. Nonlinear Analysis Hybrid Systems, 2018, 30: 106-117.
[12] CUI J, YAN L T. Asymptotic behavior for neutral stochastic partial differential equations with infinite delays [J]. Electronic Communications in Probability, 2013, 18(45): 1-12.
[13] CHEN G L, GAANS O V, LUNEL S V. Existence and exponential stability of a class of impul- sive neutral stochastic partial differential equations with delays and Poisson jumps [J]. Statistics and Probability Letters, 2018, 141: 7-18.
[14] MAO X R. Stochastic differential equations and applications[M]. Chichestic: Horwood Publishing Limited, 2007.
[15] XU Y, HE Z M. Exponential stability of neutral stochastic delay differential equations with Markovian switching [J]. Applied Mathematics Letters, 2016, 52: 64-73.
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