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Loeb Measures in Practice: Recent Advances

EMS Lectures 1997

  • Book
  • © 2000

Overview

Authors:
  1. Nigel J. Cutland
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1751)

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Table of contents (6 chapters)

  1. Front Matter

    Pages N2-xi
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  2. 1. Loeb Measures

    • Nigel J. Cutland
    Pages 1-28

  3. 2. Stochastic Fluid Mechanics

    • Nigel J. Cutland
    Pages 29-60

  4. 3. Stochastic Calculus of Variations

    • Nigel J. Cutland
    Pages 61-84

  5. 4. Mathematical Finance Theory

    • Nigel J. Cutland
    Pages 85-101

  6. References

    • Nigel J. Cutland
    Pages 103-107

  7. Index

    • Nigel J. Cutland
    Pages 109-111

  8. Back Matter

    Pages 113-117
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Keywords

About this book

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.

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