A note on the exact simulation of spherical Brownian motion
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.12107
- arXiv:
- arXiv:1811.12107
- Bibcode:
- 2018arXiv181112107M
- Keywords:
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- Mathematics - Probability
- E-Print:
- 8 pages. Added a paragraph about classical skew-product decomposition and its (un)usability for simulation of spherical Brownian motion