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Stochastic Calculus in Manifolds

  • Textbook
  • © 1989

Overview

Authors:
  1. Michel Emery

    1. UER de Mathématiques et Informatique, Université Louis Pasteur, Strasbourg Cedex, France

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Part of the book series: Universitext (UTX)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Real semimartingales and stochastic integrals

    • Michel Emery
    Pages 1-8

  3. Some vocabulary from differential geometry

    • Michel Emery
    Pages 9-20

  4. Manifold-valued semimartingales and their quadratic variation

    • Michel Emery
    Pages 21-30

  5. Connections and martingales

    • Michel Emery
    Pages 31-55

  6. Riemannian manifolds and Brownian motions

    • Michel Emery
    Pages 57-72

  7. Second order vectors and forms

    • Michel Emery
    Pages 73-89

  8. Stranovich and Itô integrals of first order forms

    • Michel Emery
    Pages 91-111

  9. Parallel transport and moving frame

    • Michel Emery
    Pages 113-127

  10. Back Matter

    Pages 129-151
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Keywords

About this book

Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic calculus. P.A. Meyer has contributed an appendix: "A short presentation of stochastic calculus" presenting the basis of stochastic calculus and thus making the book better accessible to non-probabilitists also. No prior knowledge of differential geometry is assumed of the reader: this is covered within the text to the extent. The general theory is presented only towards the end of the book, after the reader has been exposed to two particular instances - martingales and Brownian motions - in manifolds. The book also includes new material on non-confluence of martingales, s.d.e. from one manifold to another, approximation results for martingales, solutions to Stratonovich differential equations. Thus this book will prove very useful to specialists and non-specialists alike, as a self-contained introductory text or as a compact reference.

Authors and Affiliations

  • UER de Mathématiques et Informatique, Université Louis Pasteur, Strasbourg Cedex, France

    Michel Emery

Bibliographic Information

  • Book Title: Stochastic Calculus in Manifolds

  • Authors: Michel Emery

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-642-75051-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-51664-4Published: 05 January 1990

  • eBook ISBN: 978-3-642-75051-9Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: X, 151

  • Topics: Probability Theory and Stochastic Processes

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