Stochastic Calculus in Manifolds

  • Michel Emery

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Michel Emery
    Pages 31-55
  3. Michel Emery
    Pages 73-89
  4. Michel Emery
    Pages 113-127
  5. Back Matter
    Pages 129-151

About this book

Introduction

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.

Keywords

Brownian motion Christoffel symbols Martingale Riemannian manifold Semimartingale Stochastic calculus differential geometry filtration local martingale manifold quadratic variation

Authors and affiliations

  • Michel Emery
    • 1
  1. 1.UER de Mathématiques et InformatiqueUniversité Louis PasteurStrasbourg CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-75051-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-51664-4
  • Online ISBN 978-3-642-75051-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book