Stochastic Integration and Differential Equations

A New Approach

  • Philip Protter

Part of the Applications of Mathematics book series (SMAP, volume 21)

Table of contents

  1. Front Matter
    Pages I-X
  2. Philip Protter
    Pages 1-2
  3. Philip Protter
    Pages 3-42
  4. Philip Protter
    Pages 43-86
  5. Philip Protter
    Pages 87-122
  6. Philip Protter
    Pages 123-186
  7. Philip Protter
    Pages 187-284
  8. Back Matter
    Pages 285-302

About this book

Introduction

The idea of this book began with an invitation to give a course at the Third Chilean Winter School in Probability and Statistics, at Santiago de Chile, in July, 1984. Faced with the problem of teaching stochastic integration in only a few weeks, I realized that the work of C. Dellacherie [2] provided an outline for just such a pedagogic approach. I developed this into aseries of lectures (Protter [6]), using the work of K. Bichteler [2], E. Lenglart [3] and P. Protter [7], as well as that of Dellacherie. I then taught from these lecture notes, expanding and improving them, in courses at Purdue University, the University of Wisconsin at Madison, and the University of Rouen in France. I take this opportunity to thank these institut ions and Professor Rolando Rebolledo for my initial invitation to Chile. This book assumes the reader has some knowledge of the theory of stochastic processes, including elementary martingale theory. While we have recalled the few necessary martingale theorems in Chap. I, we have not provided proofs, as there are already many excellent treatments of martingale theory readily available (e. g. , Breiman [1], Dellacherie-Meyer [1,2], or Ethier­ Kurtz [1]). There are several other texts on stochastic integration, all of which adopt to some extent the usual approach and thus require the general theory. The books of Elliott [1], Kopp [1], Metivier [1], Rogers-Williams [1] and to a much lesser extent Letta [1] are examples.

Keywords

Markov Martingal Martingale Semimartingal Semimartingale Stochastic Integration boundary element method differential equation integral integration local time stability stochastic differential equation stochastische Differentialgleichungen stochastische Integration

Authors and affiliations

  • Philip Protter
    • 1
  1. 1.Mathematics and Statistics DepartmentsPurdue UniversityWest LafayetteUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02619-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02621-2
  • Online ISBN 978-3-662-02619-9
  • Series Print ISSN 0172-4568
  • Series Online ISSN 2197-439X
  • About this book