Instability and stability of solutions of systems of nonlinear stochastic difference equations with diagonal noise
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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.
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