We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length $n$ can be generated in $O(nlog\left(n\right))$ floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.

中文翻译：

---

快速正交变换和布朗路径的生成。

我们提出了许多离散布朗路径的快速构造，可用作分层蒙特卡罗和准蒙特卡罗的主成分分析和布朗桥的替代方法。我们所说的快速是指一条有长度的路径$n$ 可以在 $哦(n日志\left(n\right))$浮点运算。我们强调了不同结构之间的一些联系，并提供了一些数值示例。