We describe an exact simulation algorithm for the increments of Brownian motion on a sphere of arbitrary dimension, based on the skew-product decomposition of the process with respect to the standard geodesic distance. The radial process is closely related to a Wright-Fisher diffusion, increments of which can be simulated exactly using the recent work of Jenkins & Spano [JS17]. The rapid spinning phenomenon of the skew-product decomposition then yields the algorithm for the increments of the process on the sphere.

中文翻译：

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关于球面布朗运动精确模拟的注记

我们基于过程相对于标准测地距离的偏积分解，描述了一种用于任意维度球体上布朗运动增量的精确模拟算法。径向过程与 Wright-Fisher 扩散密切相关，可以使用 Jenkins 和 Spano [JS17] 最近的工作精确模拟其增量。偏产物分解的快速旋转现象然后产生了球体上过程增量的算法。