标题： 具有低正则性系数的随机微分方程的驯服自适应Milstein格式 显示英文标题

标题： A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients

摘要： 我们提出了一种受控自适应米尔斯坦方案，用于随机微分方程，其中系数的一阶导数在局部上是阶数为$\alpha$的霍尔德连续。我们证明了在系数满足一定增长条件的情况下，该方案在有限区间$[0, T]$和无限区间$(0, +\infty)$上以$L_2$范数的速率$(1+\alpha)/2$收敛。 显示英文摘要

摘要： 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.