Loeb Measures in Practice: Recent Advances

  • Authors
  • Nigel┬áJ.┬áCutland
Part of the Lecture Notes in Mathematics book series (LNM, volume 1751)

Table of contents

  1. Front Matter
    Pages N2-xi
  2. Nigel J. Cutland
    Pages 1-28
  3. Nigel J. Cutland
    Pages 29-60
  4. Nigel J. Cutland
    Pages 61-84
  5. Nigel J. Cutland
    Pages 85-101
  6. Nigel J. Cutland
    Pages 103-107
  7. Nigel J. Cutland
    Pages 109-111
  8. Back Matter
    Pages 113-117

About this book

Introduction

This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.

Keywords

Loeb measures Nonstandard analysis Stochastic Differential Equations Stochastic calculus calculus mathematical finance theory stochastic analysis stochastic fluid mechanics

Bibliographic information

  • DOI https://doi.org/10.1007/b76881
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-41384-4
  • Online ISBN 978-3-540-44531-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692