In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Leão et al. (??2019) and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes such as functionals of path-dependent stochastic differential equations and fractional Brownian motions. Based on statistical learning theory techniques, we provide overall error estimates in terms of concrete approximation architecture spaces with finite Vapnik-Chervonenkis dimension. Analytical properties of continuation values for path-dependent SDEs and concrete linear architecture approximating spaces are also discussed.

中文翻译：

---

非马氏最优停止问题的离散型逼近：第二部分

在本文中，我们提出了一种基于布朗运动滤波的最优停止时间问题的Longstaff-Schwartz型算法。该算法基于Leão等。（？2019），并且与以前的工作相比，我们的方法适用于完全非马氏和非半emi态状态过程的最优停止问题，例如依赖于路径的随机微分方程和分数布朗运动的函数。基于统计学习理论技术，我们根据有限Vapnik-Chervonenkis维的具体近似体系结构空间提供整体误差估计。还讨论了与路径有关的SDE和混凝土线性体系结构近似空间的连续值的分析性质。