Mixed Truncated Euler Method for Stochastic Delay Differential Equations with Concave Diffusion Coefficients

In this paper, we are concerned with strong convergence of the given mixed truncated Euler-Maruyama method for stochastic delay differential equations with concave diffusion coefficients. We prove that, when the drift term satisfies some suitable local Lipschitz and one-sided Lipschitz conditions and the diffusion term satisfies some concave condition, the mixed truncated Euler-Maruyama method strongly converges to the exact solution in the $L^p$ sense. One example is presented to interpret the theory.