24
7
v1v2v3 (latest)

Efficient Random Walks on Riemannian Manifolds

Abstract

According to a version of Donsker's theorem, geodesic random walks on Riemannian manifolds converge to the respective Brownian motion. From a computational perspective, however, evaluating geodesics can be quite costly. We therefore introduce approximate geodesic random walks based on the concept of retractions. We show that these approximate walks converge in distribution to the correct Brownian motion as long as the geodesic equation is approximated up to second order. As a result we obtain an efficient algorithm for sampling Brownian motion on compact Riemannian manifolds.

View on arXiv
Comments on this paper

We use cookies and other tracking technologies to improve your browsing experience on our website, to show you personalized content and targeted ads, to analyze our website traffic, and to understand where our visitors are coming from. See our policy.