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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Bibliographic Information

Book Title: Loeb Measures in Practice: Recent Advances
Book Subtitle: EMS Lectures 1997
Authors: Nigel J. Cutland
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b76881
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2000
Softcover ISBN: 978-3-540-41384-4Published: 12 December 2000
eBook ISBN: 978-3-540-44531-9Published: 11 October 2004
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: CXXXII, 118
Topics: Mathematical Logic and Foundations, Real Functions, Probability Theory and Stochastic Processes, Quantitative Finance

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Table of contents (6 chapters)

Front Matter

1. Loeb Measures

2. Stochastic Fluid Mechanics

3. Stochastic Calculus of Variations

4. Mathematical Finance Theory

References

Index

Back Matter

About this book