Stability and Boundedness of Stochastic Volterra Integrodifferential Equations with Infinite Delay

We make the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov-Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and boundedness of corresponding deterministic systems under some conditions

Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks

National Natural Science Foundation of China [10871120]; Natural Science Foundation of Shandong Province [Z2000A02]In this paper, we investigate the stochastic functional differential equations with infinite delay. Some sufficient conditions are derived to ensure the pth moment exponential stability and pth moment global asymptotic stability of stochastic functional differential equations with infinite delay by using Razumikhin method and Lyapunov functions. Based on the obtained results, we further study the pth moment exponential stability of stochastic recurrent neural networks with unbounded distributed delays. The result extends and improves the earlier publications. Two examples are given to illustrate the applicability of the obtained results. (C) 2010 Published by Elsevier B.V

Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties

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