This paper proposes an adaptive numerical method for stochastic delay differential equations (SDDEs) with a non-global Lipschitz drift term and a non-constant delay, building upon the work of Wei Fang and others. The method adapts the step size based on the growth of the drift term. Differing slightly from the conventional Euler-Maruyama format, this paper addresses the estimation of the delay term by substituting it with the numerically obtained solution closest to the left endpoint.This approach overcomes the challenge of numerical nodes not falling within the nodes after subtracting the delay. The paper proves the convergence of the numerical method for a class of non-global Lipschitz continuous SDDEs under the assumption that the step size function satisfies certain conditions.

翻译：本文基于Wei Fang等人的工作，针对具有非全局Lipschitz漂移项和非恒定时滞的随机时滞微分方程（SDDEs），提出了一种自适应数值方法。该方法根据漂移项的增长情况自适应调整步长。与传统的Euler-Maruyama格式略有不同，本文通过用时滞项左端点处最邻近的数值解进行替代，解决了时滞项估计的问题。这一方法克服了数值节点在减去时滞后可能不落在节点上的困难。本文证明了在步长函数满足特定条件的前提下，该数值方法对于一类非全局Lipschitz连续的SDDEs具有收敛性。