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We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs), and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM) with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration

Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations