The Stochastic -Method for Nonlinear Stochastic Volterra Integro-Differential Equations

Peng Hu and Chengming Huang

Abstract and Applied Analysis, 2014, vol. 2014, 1-13

Abstract:

The stochastic -method is extended to solve nonlinear stochastic Volterra integro-differential equations. The mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochastic -method is convergent of order in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability of the true solution is given. Under this condition, it is shown that the stochastic -method is mean-square asymptotically stable for every stepsize if and when , the stochastic -method is mean-square asymptotically stable for some small stepsizes. Finally, we validate our conclusions by numerical experiments.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:583930

DOI: 10.1155/2014/583930

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