Instability and stability of solutions of systems of nonlinear stochastic difference equations with diagonal noise - Dokuchaev, Nikolai; Rodkina, A. (Taylor & Francis, 2013)
We prove results about almost sure instability and stability of the equilibrium of asystem of nonlinear stochastic difference equation with a small parameter h. Thestructure of the system is motivated by the Euler–Maruyama discretization of an Itoˆstochastic differential equation where h is a discretization parameter. Our analysisrelies upon a variant of the discrete Itoˆ formula, which is derived for this system.