A note on the exact simulation of spherical Brownian motion
arXiv:1811.12107 · doi:10.1016/j.spl.2020.108836
Abstract
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 & Spanò (2017) [JS17]. The rapid spinning phenomenon of the skew-product decomposition then yields the algorithm for the increments of the process on the sphere.
arXiv comment8 pages. Added a paragraph about classical skew-product decomposition and its (un)usability for simulation of spherical Brownian motion
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