An Introduction to the Analysis of Paths on a Riemannian Manifold (Mathematical Surveys and Monographs) by Daniel W. Stroock (PDF)

Description

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 geometric quantities. 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 will find an inviting introduction to the study of paths and Brownian motion on Riemannian manifolds.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am a ‘hobby mathematician’ with interest in probability theory, and related subjects.This book was way over my head. I think, it was written for professional mathematicians only – far more difficult than any other book on stochastic processes, etc I have ever read.Consequently, I am in no position to judge the book.Since the shortcomings are likely mine, not the author’s, I gave full credit.

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