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100   $a20121227d2000      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aLoeb Measures in Practice: Recent Advances $eEMS Lectures 1997 /$fby Nigel J. Cutland
205   $a1st ed. 2000.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000.
215   $a1 online resource (CXXXII, 118 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1751
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-41384-7 
327   $aLoeb 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.
330   $aThis expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1751
606   $aMathematical logic
606   $aFunctions of real variables
606   $aProbabilities
606   $aEconomics, Mathematical 
606   $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005
606   $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aQuantitative Finance$3https://scigraph.springernature.com/ontologies/product-market-codes/M13062
615  0$aMathematical logic.
615  0$aFunctions of real variables.
615  0$aProbabilities.
615  0$aEconomics, Mathematical .
615 14$aMathematical Logic and Foundations.
615 24$aReal Functions.
615 24$aProbability Theory and Stochastic Processes.
615 24$aQuantitative Finance.
676   $a510
700   $aCutland$b Nigel J$4aut$4http://id.loc.gov/vocabulary/relators/aut$046036
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910144599703321
996   $aLoeb measures in practice$9262227
997   $aUNINA