Boundedness of stochastic retarded differential equations
Author:
  • Article
  • | |
  • Metrics
  • |
  • Reference [18]
  • |
  • Related [20]
  • | | |
  • Comments
    Abstract:

    In this paper,the uniform boundedness and uniform ultimate boundedness of the stochastic retarded differential equations is investigated.The new Razumikhin theorems of boundedness about these systems are obtained by using the Lyapunove functions and Razumikhin technique.It should be noted that the boundedness criteria prove the global existence of solutions as well as boundedness,thus the available results in references are improved.Finally,an example is illustrated to verify the theorems.

    Reference
    [1] Bahar A,Mao X R.Stochastic delay Lotka-Volterra model[J].J Math Anal Appl,2004,292(2):364-380
    [2] Bahar A,Mao X R.Stochastic delay population dynamics[J].International Journal of Pure and Applied Mathe-matics,2004,11(4):377-400
    [3] Bahar A,Mao X R.Persistence of stochastic power lawlogistic model[J].Journal of Applied Probability & Sta-tistics,2008,3(1):37-43
    [4] Liu S J,Ge S S,Zhang J F.Adaptive output-feedbackcontrol for a class of uncertain stochastic non-linear sys-tems with time delays[J].International Journal of Con-trol,2008,81(8):1210-1220
    [5] Blythe S,Mao X R,Liao X X.Stability of stochastic delayneural networks[J].Journal of the Franklin Institute,2001,338(4):481-495
    [6] Blythe S,Mao X R,Shah A.Razumikhin-type theoremson stability of stochastic neural networks with delay[J].Sto Anal Appl,2001,19(1):85-101
    [7] Hull J,White A.The pricing of options on assets withstochastic volatilities[J].The Journal of Finance,1987,42(2):281-300
    [8] Huang L R,Mao X R.On input-to-state stability of sto-chastic retarded systems with Markovian switching[J].IEEE Transactions on Automatic Control,2009,54 (8):1898-1902
    [9] Huang L R,Deng F Q.Razumikhin-type theorems on sta-bility of stochastic retarded systems[J].Int J SystemsScience,2009,40(1):73-80
    [10] Huang L R,Mao X R,Deng F Q.Stability of hybrid sto-chastic retarded systems[J].IEEE Trans On Circuits andSystems,2008,55(11):3413-3420
    [11] Cheng P,Deng F Q,Dai X S.Razumikhin-type theremsfor asymptotic stability of impulsive stochastic functionaldifferential system[J].J Syst Sci Syst Eng,2010,19(1):72-84
    [12] Mao X R,Rassias M J.Khasminskii-type theorems forstochastic differential delay equations[J].Sto Anal Ap-pl,2005,23(5):1045-1069
    [13] Luo Q,Mao X R,Shen Y.Generalised theory on asymp-totic stability and boundedness of stochastic functionaldifferential equations[J].Automatica,2011,47 (9):2075-2081
    [14] 吴述金,宋琼,郭小林.随机脉冲泛函微分方程的 p 阶矩有界性[J].数学物理学报,2010,30A(1):126-141WU Shujin,SONG Qiong,GUO Xiaolin.p-momentboundedness of functional differential equations with ran-dom impulses[J].Acta Mathematica Sinica,2010,30A(1):126-141
    [15] Mao X R,Yuan C G.Stochastic differential equationswith Markovian switching[M].London:Imperial CollegePress,2006
    [16] Hale J K.Theory of functional differential equations[M].New York:Springer Verlag,1977
    [17] Stamova I M.Boundedness of impulsive functional differ-ential equations with variable impulsive perturbations[J].Bull Austral Math Soc,2008,77(2):331-345
    [18] Zhang Y,Sun J T.Boundedness of the solutions of impul-sive differential systems with time-varying delay[J].Ap-pl Math Comput,2004,154(1):279-288
    Cited by
    Comments
    Comments
    分享到微博
    Submit
Get Citation

GUO Haijun, HU Junhao. Boundedness of stochastic retarded differential equations[J]. Journal of Nanjing University of Information Science & Technology,2012,4(2):180-185

Copy
Share
Article Metrics
  • Abstract:1037
  • PDF: 2454
  • HTML: 0
  • Cited by: 0
History
  • Received:January 25,2012
Article QR Code

Address:No. 219, Ningliu Road, Nanjing, Jiangsu Province

Postcode:210044

Phone:025-58731025