Abstract
We prove results about almost sure instability and stability of the equilibrium of a system of nonlinear stochastic difference equation with a small parameter h. The structure of the system is motivated by the Euler–Maruyama discretization of an Itô stochastic differential equation where h is a discretization parameter. Our analysis relies upon a variant of the discrete Itô formula, which is derived for this system.
Acknowledgements
The authors thank Dr G. Berkolaiko for his useful discussions, ARC grant of Australia DP120100928 for support of this work and anonymous referee for valuable remarks.