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.

14 pages; v3: published version

References in corpus (1)

• Geodesic random walks, diffusion processes and Brownian motion on Finsler manifolds

Cited by in corpus (1)

• Stochastic Modified Flows for Riemannian Stochastic Gradient Descent