Skew-product decomposition of Brownian motion on an ellipsoid

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.