Loeb Measures in Practice: Recent Advances

EMS Lectures 1997

Nigel J. Cutland (Autor)

Buch | Softcover

CXXXII, 118 Seiten

2000
Springer Berlin (Verlag)
978-3-540-41384-4 (ISBN)

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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.

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

Erscheint lt. Verlag	12.12.2000
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	CXXXII, 118 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	195 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Schlagworte	Calculus • Loeb measures • mathematical finance theory • nonstandard analysis • Quantitative Finance • stochastic analysis • Stochastic Calculus • Stochastic differential equations • stochastic fluid mechanics
ISBN-10	3-540-41384-7 / 3540413847
ISBN-13	978-3-540-41384-4 / 9783540413844
Zustand	Neuware