A Milstein-type method is proposed for some highly non-linear non-autonomous time-changed stochastic differential equations (SDEs). The spatial variables in the coefficients of the time-changed SDEs satisfy the super-linear growth condition and the temporal variables obey some H\"older's continuity condition. The strong convergence in the finite time is studied and the convergence order is obtained.

翻译：针对一类高度非线性非自治时间变换随机微分方程（SDEs），本文提出了一种 Milstein 型方法。时间变换 SDEs 系数中的空间变量满足超线性增长条件，时间变量服从某种 Hölder 连续性条件。文中研究了有限时间内的强收敛性，并得出了收敛阶。