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Stochastic calculus with infinitesimals / Frederik S. Herzberg.

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Author/Creator:
Herzberg, Frederik, 1981- author.
Language:
English
Publication:
Heidelberg : Springer, [2013]
Copyright notice:
©2013
Format:
  • Book
  • xviii, 112 pages ; 24 cm.
Bibliography:
Includes bibliographical references (pages 107-110) and index.
Contents:
  • Infinitesimal calculus, consistently and accessibly
  • Radically elementary probability theory
  • Radically elementary stochastic integrals
  • The radically elementary Girsanov theorem and the diffusion invariance principle
  • Excursion to financial economics: a radically elementary approach to the fundamental theorems of asset pricing
  • Excursion to financial engineering: volatility invariance in the Black-Scholes model
  • A radically elementary theory of Itô diffusions and associated partial differential equations
  • Excursion to mathematical physics: a radically elementary definition of Feynman path integrals
  • A radically elementary theory of Lévy processes
  • Excursion to logic: some remarks on the metamathematics of minimal internal set theory
  • Robinsonian vs. minimal nonstandard analysis.
Summary:
"This short monograph develops basic stochastic analysis ... and select applications in the framework of Edward Nelson's 'Radically elementary probability theory' (Annals of mathematics studies, 117, Princeton, NJ : Princeton University Press, 1987). This approach requires neither measure-theoretic probability theory nor functional analysis, but is based on a rigorous, yet elementary use of unlimited natural numbers and infinitesimals."-- Abstract.
Series:
Lecture notes in mathematics, 0075-8434 ; 2067
Lecture notes in mathematics (Springer-Verlag) ; 2067.
Subjects:
ISBN:
9783642331480
3642331483

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