Classical approximation results for stochastic differential equations analyze the $L^p$-distance between the exact solution and its Euler-Maruyama approximations. In this article we measure the error with temporal-spatial H\"older-norms. Our motivation for this are multigrid approximations of the exact solution viewed as a function of the starting point. We establish the classical strong convergence rate $0.5$ with respect to temporal-spatial H\"older-norms if the coefficient functions have bounded derivatives of first and second order.
翻译：Stochactic 差分方程的经典近似结果分析了 $L $p$- 准确解决方案与 欧拉- 丸山近似值之间的距离。 在本条中, 我们用时间空间 H\ “ older- norms ” 测量错误。 我们这样做的动机是将精确解决方案视为起点函数的多电离近似值。 如果系数函数将第一和第二顺序的衍生物捆绑在一起, 我们就可以确定时间空间 H\ “ older- norms” 的典型强烈趋同率 0. 5美元 。
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