Almost sure asymptotic stability analysis of the -Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations
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AbstractWe perform an almost surelinear stability analysis of the -Maruyama method, selecting as our test equation a two-dimensional system of It differential equations with diagonal drift coefficient and two independent stochastic perturbations which capture the stabilising and destabilising roles of feedback geometry in the almost sureasymptotic stability of the equilibrium solution. For small values of the constant step-size parameter, we derive close-to-sharp conditions for the almost sureasymptotic stability and instability of the equilibrium solution of the discretisation that match those of the original test system. Our investigation demonstrates the use of a discrete form of the It formula in the context of an almost surelinear stability analysis.
