Stochastic Integration and Differential Equations

  • Philip E. Protter

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 21)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Philip E. Protter
    Pages 1-2
  3. Philip E. Protter
    Pages 3-49
  4. Philip E. Protter
    Pages 51-100
  5. Philip E. Protter
    Pages 101-154
  6. Philip E. Protter
    Pages 155-248
  7. Philip E. Protter
    Pages 249-361
  8. Philip E. Protter
    Pages 363-396
  9. Back Matter
    Pages 397-421

About this book

Introduction

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach".

The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emeryâ¬(tm)s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.

Keywords

Brownian motion Girsanov theorem Martingale Poisson process Semimartingale filtration local martingale local time

Authors and affiliations

  • Philip E. Protter
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-10061-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05560-7
  • Online ISBN 978-3-662-10061-5
  • Series Print ISSN 0172-4568
  • About this book