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An Introduction to the Analysis of Paths on a Riemannian Manifold (Mathematical Surveys and Monographs) 🔍
Daniel W. Stroock R.I. : American Mathematical Society, Mathematical surveys and monographs, no. 74, Providence, R.I, ©2000
English [en] · PDF · 7.1MB · 2000 · 📘 Book (non-fiction) · 🚀/duxiu/lgli/lgrs/nexusstc/upload/zlib · Save
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.
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zlib/Mathematics/Daniel W. Stroock/An Introduction to the Analysis of Paths on a Riemannian Manifold (Mathematical Surveys and Monographs)_1104694.pdf
Alternative title
An introduction to the analysis of paths on a Riemannian manifold volume 74
Alternative author
Acrobat 5.0 Scan Plug-in for Windows
Alternative author
Stroock, Daniel W.
Alternative edition
Mathematical surveys and monographs, Erscheinungsort nicht ermittelbar, 2005
Alternative edition
American Mathematical Society, Providence, R.I., 2000
Alternative edition
United States, United States of America
Alternative edition
UK ed., 2005-03-24
Alternative edition
November 1999
Alternative edition
1, 2000
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до 2011-08
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lg665765
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producers:
Acrobat 5.0 Scan Plug-in for Windows
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{"isbns":["0821820206","0821838393","9780821820209","9780821838396"],"last_page":279,"publisher":"American Mathematical Society","series":"Mathematical Surveys and Monographs 74"}
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类型: 图书
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出版日期: 2005.03
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出版社: Amer Mathematical Society
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页码: 269
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出版日期: 2000
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出版社: American Mathematical Society
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页码: 270
Alternative description
Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR
Alternative description
In order for a mathematician to take A. Einstein's 1905 article [12] seriously, he should feel obliged to begin by doing what N. Wiener did in his 1923 article [45].
date open sourced
2011-08-31
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