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Aspects of Stochastic Global Analysis

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From Geometry to Quantum Mechanics

Part of the book series: Progress in Mathematics ((PM,volume 252))

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Abstract

This is a survey of some topics where global and stochastic analysis play a role. An introduction to analysis on Banach spaces with Gaussian measure leads to an analysis of the geometry of stochastic differential equations, stochastic flows, and their associated connections, with reference to some related topological vanishing theorems. Following that, there is a description of the construction of Sobolev calculi over path and loop spaces with diffusion measures, and also of a possible L 2 de Rham and Hodge-Kodaira theory on path spaces. Diffeomorphism groups and diffusion measures on their path spaces are central to much of the discussion. Knowledge of stochastic analysis is not assumed.

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Authors and Affiliations

  1. Mathematics Institute, Warwick University, Coventry, CV4 7AL, England

    K. D. Elworthy

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  1. K. D. Elworthy
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Editors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, 223-8522, Japan

    Yoshiaki Maeda

  2. Department of Natural Science, Nippon Sports Science University, 7-1-1, Fukazawa, Setagaya-ku, Tokyo, 158-8508, Japan

    Takushiro Ochiai

  3. Facultät für Mathematik, Universität Wein, Nordbergstrasse 15, A-1090, Wein, Austria

    Peter Michor

  4. Department of Mathematics, Tokyo University of Science, Kagurazaka, Tokyo, 102-8601, Japan

    Akira Yoshioka

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Dedicated to Hideki Omori

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Elworthy, K.D. (2007). Aspects of Stochastic Global Analysis. In: Maeda, Y., Ochiai, T., Michor, P., Yoshioka, A. (eds) From Geometry to Quantum Mechanics. Progress in Mathematics, vol 252. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4530-4_1

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