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008 121116s2013 gw | s |||| 0|eng d
020 _a9783642331497
_9978-3-642-33149-7
024 7 _a10.1007/978-3-642-33149-7
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aPBCD
_2bicssc
072 7 _aMAT018000
_2bisacsh
082 0 4 _a511.3
_223
100 1 _aHerzberg, Frederik.
_eauthor.
245 1 0 _aStochastic Calculus with Infinitesimals
_h[electronic resource] /
_cby Frederik Herzberg.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXVIII, 112 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 ;
_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 _aMathematics.
650 0 _aGame theory.
650 0 _aMathematical logic.
650 0 _aProbabilities.
650 0 _aMathematical physics.
650 0 _aEconomic theory.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aEconomic Theory/Quantitative Economics/Mathematical Methods.
650 2 4 _aGame Theory, Economics, Social and Behav. Sciences.
650 2 4 _aMathematical Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642331480
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2067
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-33149-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
942 _2Dewey Decimal Classification
_ceBooks
999 _c46277
_d46277