Loeb Measures in Practice: Recent Advances

EMS Lectures 1997

AvNigel J. Cutland

Häftad, Engelska, 2000

Del 1751 i serien Lecture Notes in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2000-12-12
Mått:155 x 235 x 8 mm
Vikt:211 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:118
Upplaga:2000
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540413844

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Innehållsförteckning

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