04567nam 22007095 450 99646677150331620200630031401.03-642-33149-110.1007/978-3-642-33149-7(CKB)3400000000102775(SSID)ssj0000810092(PQKBManifestationID)11456156(PQKBTitleCode)TC0000810092(PQKBWorkID)10826405(PQKB)11180734(DE-He213)978-3-642-33149-7(MiAaPQ)EBC3070794(PPN)168323672(EXLCZ)99340000000010277520121116d2013 u| 0engurnn|008mamaatxtccrStochastic Calculus with Infinitesimals[electronic resource] /by Frederik S. Herzberg1st ed. 2013.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2013.1 online resource (XVIII, 112 p.) Lecture Notes in Mathematics,0075-8434 ;2067Bibliographic Level Mode of Issuance: Monograph3-642-33148-3 Includes bibliographical references (p.107-110) and index.1 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.Stochastic 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.Lecture Notes in Mathematics,0075-8434 ;2067Mathematical logicProbabilitiesEconomic theoryGame theoryMathematical physicsMathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Economic Theory/Quantitative Economics/Mathematical Methodshttps://scigraph.springernature.com/ontologies/product-market-codes/W29000Game Theory, Economics, Social and Behav. Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13011Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Mathematical logic.Probabilities.Economic theory.Game theory.Mathematical physics.Mathematical Logic and Foundations.Probability Theory and Stochastic Processes.Economic Theory/Quantitative Economics/Mathematical Methods.Game Theory, Economics, Social and Behav. Sciences.Mathematical Physics.511.3Herzberg Frederik Sauthttp://id.loc.gov/vocabulary/relators/aut521683BOOK996466771503316Stochastic calculus with infinitesimals837746UNISA