Global Asymptotic Stability of Solutions of Cubic Stochastic Difference Equations
نویسنده
چکیده
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 R1. As an application of this result, the asymptotic stability of stochastic numerical methods, such as partially drift-implicit θ-methods with variable step sizes for ordinary stochastic differential equations driven by standard Wiener processes, is discussed.
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تاریخ انتشار 2004