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020 _a9783540445319
_9978-3-540-44531-9
024 7 _a10.1007/b76881
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aMAT018000
_2bisacsh
072 7 _aPBC
_2thema
072 7 _aPBCD
_2thema
082 0 4 _a511.3
_223
100 1 _aCutland, Nigel J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLoeb Measures in Practice: Recent Advances
_h[electronic resource] /
_cby Nigel J. Cutland.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2000.
300 _aCXXXII, 118 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1751
505 0 _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.
520 _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.
650 0 _aLogic, Symbolic and mathematical.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory.
650 0 _aFinance.
650 1 4 _aMathematical Logic and Foundations.
_0http://scigraph.springernature.com/things/product-market-codes/M24005
650 2 4 _aReal Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M12171
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aQuantitative Finance.
_0http://scigraph.springernature.com/things/product-market-codes/M13062
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662211908
776 0 8 _iPrinted edition:
_z9783540413844
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1751
856 4 0 _uhttps://doi.org/10.1007/b76881
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10420
_d10420