Rodkina, Alexandra E.; Schurz, Henri
Author Affiliation, Ana.
Department of Mathematics and Computer Science
Global asymptotic stability of solutions to cubic stochastic difference equations
Advances in difference equations
Date of Publication
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 ?-methods with variable step sizes for ordinary stochastic differential equations driven by standard Wiener processes, is discussed.....