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Lecture Notes in Mathematics Ser.: Stochastic Calculus with Infinitesimals by Frederik S. Herzberg (2012, Trade Paperback)
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103642331483
ISBN-139783642331480
eBay Product ID (ePID)144056326
Product Key Features
Number of PagesXviii, 112 Pages
Publication NameStochastic Calculus with Infinitesimals
LanguageEnglish
Publication Year2012
SubjectDifferential Equations / General, Probability & Statistics / Stochastic Processes, Probability & Statistics / General, Econometrics, Logic
TypeTextbook
AuthorFrederik S. Herzberg
Subject AreaMathematics, Business & Economics
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight74.7 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2012-951626
Dewey Edition23
Series Volume Number2067
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal519.22
Table Of Content1 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.
Synopsis1 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.
LC Classification NumberQA8.9-10.3
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