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International Journal of Systems Science Volume 43, 2012 - Issue 2
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Original Articles

Stochastic stability of a class of unbounded delay neutral stochastic differential equations with general decay rate

Yangzi Hu School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
,
Fuke Wu School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R. ChinaCorrespondence[email protected]
&
Chengming Huang School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
Pages 308-318 | Received 01 Aug 2009, Accepted 25 Apr 2010, Published online: 26 Nov 2010

References

  • Appleby , JAD . 2005 . Decay and Growth Rates of Solutions of Scalar Stochastic Delay Differential Equations with Unbounded Delay and State Dependent Noise . Stochastics and Dynamics , 5 : 133 – 147 .
  • Appleby, J.A.D., and Buckwar, E. (2003), ‘Sufficient Condition for Polynomial Asymptotic Behaviour of Stochastic Pantograph Equations’, www.dcu.ie/maths/research/preprints.
  • Arnold , L . 1972 . Stochastic Differential Equations: Theory and Applications , New York : Wiley .
  • Baker , CTH and Buckwar , E . 2000 . Continuous θ-Methods for the Stochastic Pantograph Equation . Electronic Transactions on Numerical Analysis , 11 : 131 – 151 .
  • Berman , A and Plemmons , RJ . 1994 . Nonnegative Matrices in the Mathematical Sciences , Philadelphia, PA : SIAM .
  • Caraballo , T , Garrido-Atienza , MJ and Real , J . 2003 . Stochastic Stabilization of Differential Systems with General Decay Rate . Systems and Control Letters , 48 : 397 – 406 .
  • Deng , F , Luo , Q , Mao , X and Pang , S . 2008 . Noise Suppresses or Expresses Exponential Growth . Systems and Control Letters , 57 : 262 – 270 .
  • Fan , Z , Liu , M and Cao , W . 2007 . Existence and Uniqueness of the Solutions and Convergence of Semi-implicit Euler Methods for Stochastic Pantograph Equations . Journal of Mathematical Analysis and Applications , 325 : 1142 – 1159 .
  • Liu , K and Mao , X . 2001 . Large Time Decay Behavior of Dynamical Equations with Random Perturbation Features . Stochastic Analysis and Applications , 19 : 295 – 327 .
  • Liptser , RSh and Shiryaev , AN . 1989 . Theory of Martingale , Dordrecht : Kluwer Academic .
  • Mao , X . 1992 . Almost Sure Polynomial Stability for a Class of Stochastic Differential Equations . Quarterly Journal of Mathematics Oxford , 43 : 339 – 348 .
  • Mao , X . 1994 . Exponential Stability of Stochastic Differential Equations , New York : Marcel, Dekker . 1994
  • Mao , X . 1995 . Exponential Stability in Mean Square of Neutral Stochastic Differential Functional Equations . Systems and Control Letters , 26 : 245 – 251 .
  • Mao , X . 1997a . Razumikhin-type Theorems on Exponential Stability of Neutral Stochastic Functional Differential . SIAM Journal on Mathematical Analysis , 28 : 389 – 401 .
  • Mao , X . 1997b . Stochastic Differential Equations and Applications , Chichester : Horwood .
  • Mao , X . 2002 . A Note on the Lasalle-type Theorems for Stochastic Differential Delay Equations . Journal of Mathematical Analysis and Applications , 268 : 125 – 142 .
  • Randjelović , J and Janković , S . 2007 . On the pth Moment Exponential Stability Criteria of Neutral Stochastic Functional Differential Equations . Journal of Mathematical Analysis and Applications , 326 : 266 – 280 .

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