Global asymptotic stability of solutions of cubic stochastic difference equations
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2004-07-12
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Abstract
Global almost sure asymptotic stability of solutions of some nonlinear stochastic difference equations with cubic-type main part in their drift and diffusive part driven by square-integrable martingale differences is proven under appropriate conditions in and#8477;1. As an application of this result, the asymptotic stability of stochastic numerical methods, such as partially drift-implicit and#952;-methods with variable step sizes for ordinary stochastic differential equations driven by standard Wiener processes, is discussed.
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Advances in Difference Equations. 2004 Jul 12;2004(3):513569