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Advances in Continuous and Discrete Models

Theory and Modern Applications

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Global asymptotic stability of solutions of cubic stochastic difference equations

Advances in Difference Equations volume 2004, Article number: 513569 (2004) Cite this article

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 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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of the West Indies at Mona, Kingston 7, Jamaica

    Alexandra Rodkina

  2. Department of Mathematics, Southern Illinois University, 1245 Lincoln Drive, Carbondale, IL, 62901-4408, USA

    Henri Schurz

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  1. Alexandra Rodkina
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  2. Henri Schurz
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Correspondence to Alexandra Rodkina.

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Rodkina, A., Schurz, H. Global asymptotic stability of solutions of cubic stochastic difference equations. Adv Differ Equ 2004, 513569 (2004). https://doi.org/10.1155/S1687183904309015

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  • DOI: https://doi.org/10.1155/S1687183904309015