000 | 03863nam a22005415i 4500 | ||
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001 | 978-3-540-44531-9 | ||
003 | DE-He213 | ||
005 | 20190213151349.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s2000 gw | s |||| 0|eng d | ||
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_a9783540445319 _9978-3-540-44531-9 |
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024 | 7 |
_a10.1007/b76881 _2doi |
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_aPBC _2bicssc |
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_aMAT018000 _2bisacsh |
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_aPBC _2thema |
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_aPBCD _2thema |
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_a511.3 _223 |
100 | 1 |
_aCutland, Nigel J. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aCXXXII, 118 p. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1751 |
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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 |