A Euler's type method with the equidistant step size is proposed for a class of time-changed stochastic differential equations driven by the multiplicative noise and the strong convergence rate that is related to the parameter of the time changing process is obtained. Such a observation of the convergence rate is significantly different from those existing results that employ methods with the random step size. The polynomial stability in the mean square sense of the numerical method is also studied, which is in line with the asymptotic behavior of the underlying equation.

翻译：针对一类由乘性噪声驱动的时间变换随机微分方程，本文提出了一种等步长的欧拉型方法，并获得了与时间变换过程参数相关的强收敛率。这种收敛率的观测结果与采用随机步长方法的现有研究存在显著差异。同时，本文研究了该数值方法在均方意义下的多项式稳定性，该稳定性与原方程的渐近行为保持一致。