We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally H\"older continuous of order $\alpha$. We show that the scheme converges in the $L_2$-norm with a rate of $(1+\alpha)/2$ over both finite intervals $[0, T]$ and the infinite interval $(0, +\infty)$, under certain growth conditions on the coefficients.

翻译：针对一阶导数具有局部$\alpha$阶H\"older连续系数的随机微分方程，我们提出了一种驯服自适应Milstein格式。我们证明，在系数满足特定增长条件下，该格式在有限区间$[0, T]$和无限区间$(0, +\infty)$上均能以$(1+\alpha)/2$的速率按$L_2$范数收敛。