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2014 A Class of Stochastic Nonlinear Delay System with Jumps
Ling Bai, Kai Zhang, Wenju Zhao
J. Appl. Math. 2014: 1-11 (2014). DOI: 10.1155/2014/458306


We consider stochastic suppression and stabilization for nonlinear delay differential system. The system is assumed to satisfy local Lipschitz condition and one-side polynomial growth condition. Since the system may explode in a finite time, we stochastically perturb this system by introducing independent Brownian noises and Lévy noise feedbacks. The contributions of this paper are as follows. (a) We show that Brownian noises or Lévy noise may suppress potential explosion of the solution for some appropriate parameters. (b) Using the exponential martingale inequality with jumps, we discuss the fact that the sample Lyapunov exponent is nonpositive. (c) Considering linear Lévy processes, by the strong law of large number for local martingale, sufficient conditions for a.s. exponentially stability are investigated in Theorem 13.


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Ling Bai. Kai Zhang. Wenju Zhao. "A Class of Stochastic Nonlinear Delay System with Jumps." J. Appl. Math. 2014 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07010640
MathSciNet: MR3166764
Digital Object Identifier: 10.1155/2014/458306

Rights: Copyright © 2014 Hindawi


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