Open Access

Global asymptotic stability of solutions of cubic stochastic difference equations

Advances in Difference Equations20042004:513569

DOI: 10.1155/S1687183904309015

Received: 18 September 2003

Published: 12 July 2004

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 1. 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.

Authors’ Affiliations

(1)
Department of Mathematics and Computer Science, University of the West Indies at Mona
(2)
Department of Mathematics, Southern Illinois University

Copyright

© Rodkina and Schurz 2004