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

279 Pages·2000·6.747 MB·English
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by Daniel W. Stroock| 2000| 279 pages| 6.747| English

About 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 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.

Detailed Information

Author:Daniel W. Stroock
Publication Year:2000
ISBN:9780821838396
Pages:279
Language:English
File Size:6.747
Format:PDF
Price:FREE
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