Loeb Measures in Practice: Recent Advances / by Nigel J. Cutland
(Lecture Notes in Mathematics ; 1751)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 2000 |
| 本文言語 | 英語 |
| 大きさ | CXXXII, 118 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Cutland, Nigel J. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Functions of real variables LCSH:Economics, Mathematical LCSH:Mathematical logic LCSH:Probabilities FREE:Mathematics FREE:Mathematical Logic and Foundations FREE:Real Functions FREE:Probability Theory and Stochastic Processes FREE:Quantitative Finance |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9783540445319 
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| ISBN | 9783540445319 |
| URL | http://dx.doi.org/10.1007/b76881 |
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