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arXiv · 1811.12107

A note on the exact simulation of spherical Brownian motion

Aleksandar Mijatović·Veno Mramor·Gerónimo Uribe Bravo
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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 & Span\`{o} (2017) [JS17]. The rapid spinning phenomenon of the skew-product decomposition then yields the algorithm for the increments of the process on the sphere.

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Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo. 2018-11-29. A note on the exact simulation of spherical Brownian motion. https://doi.org/10.1016/j.spl.2020.108836

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