An Introduction to the Analysis of Paths on a Riemannian Manifold - Mathematical Surveys and Monographs

Presents a study of paths and Brownian motion on Riemannian manifolds. This book offers two constructions of Brownian motion on a Riemannian manifold: an extrinsic one where the manifold is realized as an embedded sub manifold of Euclidean space and an intrinsic one based on the 'rolling' map.