Stability in Probability of Nonlinear Stochastic Volterra Difference Equations with Continuous Variable |
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Authors: | Jiaowan Luo Leonid Shaikhet |
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Affiliation: | 1. School of Mathematics and Information Science, Guangzhou University , Guangzhou, P.R. China mathluo@yahoo.com;3. Department of Higher Mathematics , Donetsk State University of Management , Donetsk, Ukraine |
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Abstract: | Abstract The general method of Lyapunov functionals construction, that was proposed by Kolmanovskii and Shaikhet and successfully used already for functional-differential equations, difference equations with discrete time, difference equations with continuous time, and is used here to investigate the stability in probability of nonlinear stochastic Volterra difference equations with continuous time. It is shown that the investigation of the stability in probability of nonlinear stochastic difference equation with order of nonlinearity more than one can be reduced to investigation of the asymptotic mean square stability of the linear part of this equation. |
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Keywords: | Asymptotic mean square stability Continuous variable Method of Lyapunov functionals construction Nonlinear stochastic Volterra difference equations Stability in probability |
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