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The strong convergence of Euler approximations of stochastic delaydifferential equations is proved under general conditions. The assumptions ondrift and diffusion coefficients have been relaxed to include polynomial growthand only continuity in the arguments corresponding to delays. Furthermore, therate of convergence is obtained under one-sided and polynomial Lipschitzconditions. Finally, our findings are demonstrated with the help of numericalsimulations.

Strong Convergence of Euler Approximations of Stochastic Differential Equations with Delay under Local Lipschitz Condition