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

This book aims to bridge the gap between probability and differential geometry. It gives two constructions of Brownian motion on a Riemannian manifold: an extrinsic one where the manifold is realized as an embedded submanifold of Euclidean space and an intrinsic one based on the ''rolling'' map. It is then shown how geometric quantities (such as curvature) are reflected by the behavior of Brownian paths and how that behavior can be used to extract information about geometricquantities. Readers should have a strong background in analysis with basic knowledge in stochastic calculus and differential geometry. Professor Stroock is a highly-respected expert in probability and analysis. The clarity and style of his exposition further enhance the quality of this volume. Readers willfind an inviting introduction to the study of paths and Brownian motion on Riemannian manifolds.Daniel W. Stroock is the author of 'An Introduction to the Analysis of Paths on a Riemannian Manifold (Mathematical Surveys and Monographs)', published 2005 under ISBN 9780821838396 and ISBN 0821838393.