Loeb Measures in Practice: Recent Advances
EMS Lectures 1997
Published on 12. December 2000
Book
Paperback/Softback
CXXXII, 118 pages
978-3-540-41384-4 (ISBN)
Description
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.
More details
Series
Edition
2000 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
CXXXII, 118 p.
Dimensions
Height: 233 mm
Width: 155 mm
Thickness: 8 mm
Weight
211 gr
ISBN-13
978-3-540-41384-4 (9783540413844)
DOI
10.1007/b76881
Schweitzer Classification
Other editions
Additional editions
E-Book
10/2004
Springer
€35.30
Available for download
Content
Loeb Measures: Introduction.- Nonstandard Analysis.- Construction of Loeb Measures.- Loeb Integration Theory.- Elementary Applications. Stochastic Fluid Mechanics: Introduction.- Solution of the Deterministic Navier-Stokes Equations.- Solution of the Stochastic Navier-Stokes Equations.- Stochastic Euler Equations.- Statistical Solutions.- Attractors for the Navier-Stokes Equations.- Measure Attractors for Stochastic Navier-Stokes Equations.- Stochastic Attractors for Navier-Stokes Equations.- Attractors for the 3-dimensional Stochastic Navier-Stokes Equations. Stochastic Calculus of Variations: Introduction.- Flat Integral Representation of Wiener Measure.- The Wiener Sphere.- Brownian Motion on the Wiener Sphere and the Infinite Dimensional Ornstein-Uhlenbeck Process.- Malliavin Calculus. Mathematical Finance Theory: Introduction.- The Cox-Ross-Rubinstein Models.- Options and Contingent Claims.- The Black-Scholes Model...
The complete table of contents can be found on the Internet: http://www.springer.de
The complete table of contents can be found on the Internet: http://www.springer.de