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100   $a20121116d2013      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aStochastic Calculus with Infinitesimals$b[electronic resource] /$fby Frederik S. Herzberg
205   $a1st ed. 2013.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013.
215   $a1 online resource (XVIII, 112 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2067
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-33148-3 
320   $aIncludes bibliographical references (p.107-110) and index.
327   $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.
330   $aStochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2067
606   $aMathematical logic
606   $aProbabilities
606   $aEconomic theory
606   $aGame theory
606   $aMathematical physics
606   $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000
606   $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
615  0$aMathematical logic.
615  0$aProbabilities.
615  0$aEconomic theory.
615  0$aGame theory.
615  0$aMathematical physics.
615 14$aMathematical Logic and Foundations.
615 24$aProbability Theory and Stochastic Processes.
615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods.
615 24$aGame Theory, Economics, Social and Behav. Sciences.
615 24$aMathematical Physics.
676   $a511.3
700   $aHerzberg$b Frederik S$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521683
906   $aBOOK
912   $a996466771503316
996   $aStochastic calculus with infinitesimals$9837746
997   $aUNISA