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Loeb Measures in Practice: Recent Advances de Nigel J. Cutland

Loeb Measures in Practice: Recent Advances: Lecture Notes in Mathematics, cartea 1751

Autor Nigel J. Cutland
en Limba Engleză Paperback – 12 dec 2000
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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Specificații

ISBN-13: 9783540413844
ISBN-10: 3540413847
Pagini: 132
Ilustrații: CXXXII, 118 p.
Dimensiuni: 155 x 233 x 8 mm
Greutate: 0.21 kg
Ediția:2000
Editura: Springer
Colecția Lecture Notes in Mathematics
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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