The strong $L^2$-approximation of occupation time functionals is studied with respect to discrete observations of a $d$-dimensional c\`adl\`ag process. Upper bounds on the error are obtained under weak assumptions, generalizing previous results in the literature considerably. The approach relies on regularity for the marginals of the process and applies also to non-Markovian processes, such as fractional Brownian motion. The results are used to approximate occupation times and local times. For Brownian motion, the upper bounds are shown to be sharp up to a log-factor.

翻译：在对一个以美元计数的c ⁇ adl ⁇ ag过程的离散观测方面,对占用时间功能的强烈接近值为2美元的研究。错误的上界是在虚弱的假设下取得的,在文献中大量概括了以前的结果。该方法依赖于该过程边缘的规律性,也适用于非马尔科文过程,例如分数的布朗运动。结果用于大约占用时间和当地时间。对于Brownian运动来说,上界线显示是尖锐到日志因子的。