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Graduate Studies in Mathematics Ser.: Stochastic Analysis on Manifolds by Elton P. Hsu (2002, Hardcover)

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Product Description : Mainly from the perspective of a probabilist Hsu shows how stochastic analysis and differential geometry can work together for their mutual benefit He writes for researchers and advanced graduate students with a firm foundation in basic euclidean stochastic analysis and differential geometry He does not include the exercises usual to such texts but does provide proofs throughout that invite readers to test their understanding Annotation c Book News Inc Portland OR booknewscom

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Probability theory has become a convenient language and a useful tool in many areas of modern analysis. The main purpose of this book is to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A dominant theme of the book is the probabilistic interpretation of the curvature of a manifold.