Loeb Measures in Practice: Recent Advances [[electronic resource] ] : EMS Lectures 1997 / / by Nigel J. Cutland

• Autore: Cutland Nigel J
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
• Edizione: 1st ed. 2000.
• Descrizione fisica: 1 online resource (CXXXII, 118 p.)
• Disciplina: 510
• Soggetto topico: Mathematical logic; Functions of real variables; Probabilities; Economics, Mathematical ; Mathematical Logic and Foundations; Real Functions; Probability Theory and Stochastic Processes; Quantitative Finance
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Loeb measures in practice
• ISBN: 3-540-44531-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910144599703321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1751