Stochastic Calculus in Manifolds / Edition 1

by Michel Emery

Overview

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 shastic calculus. P.A. Meyer has contributed an appendix: "A short presentation of shastic calculus" presenting the basis of shastic 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.

Product Details

ISBN-13:	9783540516644
Publisher:	Springer Berlin Heidelberg
Publication date:	12/18/1989
Series:	Universitext
Edition description:	Softcover reprint of the original 1st ed. 1989
Pages:	151
Product dimensions:	6.69(w) x 9.53(h) x 0.02(d)

Table of Contents

I. Real semimartingales and shastic integrals.- II. Some vocabulary from differential geometry.- III. Manifold-valued semimartingales and their quadratic variation.- IV. Connections and martingales.- V. Riemannian manifolds and Brownian motions.- VI. Second order vectors and forms.- VII. Stratonovich and Itô integrals of first order forms.- VIII. Parallel transport and moving frame.- Appendix: A short presentation of shastic calculus.

Editorial Reviews

The phrase "Brownian motion in curved space" may serve to suggest the problem area to which this slim monograph (evolved from lectures presented in 1985 and 1986 in Lausanne and Shanghai) is addressed. The author's intent is pedagogical, but his mathematical style is very French, with the consequence that mathematicians are likely to find the book a good deal more accessible than the physicists who might otherwise have interest in its contents. Presented as a 23-page appendix is "A short presentation of stochastic calculus", by P.A. Meyer. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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