Skew-product decomposition of Brownian motion on an ellipsoid

Ivana Valentić

Statistics & Probability Letters, 2023, vol. 195, issue C

Abstract: In this article we obtain a skew-product decomposition of a Brownian motion on an ellipsoid of dimension n in a Euclidean space of dimension n+1. We only consider such ellipsoid whose restriction to first n dimensions is a sphere and its last coordinate depends on a variable parameter. We prove that the projection of this Brownian motion on to the last coordinate is, after a suitable transformation, a Wright–Fisher diffusion process with atypical selection coefficient.

Keywords: Skew-product decomposition; Brownian motion on a manifold; Wright–Fisher diffusion (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109784

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