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003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 121116s2013 gw | s |||| 0|eng d | ||
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_a9783642331497 _9978-3-642-33149-7 |
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_a10.1007/978-3-642-33149-7 _2doi |
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_aPBC _2bicssc |
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_aPBCD _2thema |
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_a511.3 _223 |
100 | 1 |
_aHerzberg, Frederik. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aStochastic Calculus with Infinitesimals _h[electronic resource] / _cby Frederik Herzberg. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013. |
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300 |
_aXVIII, 112 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2067 |
|
505 | 0 | _a1 Infinitesimal calculus, consistently and accessibly -- 2 Radically elementary probability theory -- 3 Radically elementary stochastic integrals -- 4 The radically elementary Girsanov theorem and the diffusion invariance principle -- 5 Excursion to nancial economics: A radically elementary approach to the fundamental theorems of asset pricing -- 6 Excursion to financial engineering: Volatility invariance in the Black-Scholes model -- 7 A radically elementary theory of Itô diffusions and associated partial differential equations -- 8 Excursion to mathematical physics: A radically elementary definition of Feynman path integrals -- 9 A radically elementary theory of Lévy processes -- 10 Final remarks. | |
520 | _aStochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book. | ||
650 | 0 | _aLogic, Symbolic and mathematical. | |
650 | 0 | _aDistribution (Probability theory. | |
650 | 0 | _aEconomic theory. | |
650 | 0 | _aMathematics. | |
650 | 1 | 4 |
_aMathematical Logic and Foundations. _0http://scigraph.springernature.com/things/product-market-codes/M24005 |
650 | 2 | 4 |
_aProbability Theory and Stochastic Processes. _0http://scigraph.springernature.com/things/product-market-codes/M27004 |
650 | 2 | 4 |
_aEconomic Theory/Quantitative Economics/Mathematical Methods. _0http://scigraph.springernature.com/things/product-market-codes/W29000 |
650 | 2 | 4 |
_aGame Theory, Economics, Social and Behav. Sciences. _0http://scigraph.springernature.com/things/product-market-codes/M13011 |
650 | 2 | 4 |
_aMathematical Physics. _0http://scigraph.springernature.com/things/product-market-codes/M35000 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783642331480 |
776 | 0 | 8 |
_iPrinted edition: _z9783642331503 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2067 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-642-33149-7 |
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912 | _aZDB-2-LNM | ||
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