Lecture Notes in Mathematics

Stochastic Calculus with Infinitesimals

Authors: Herzberg, Frederik S.

  • A demonstrably consistent use of infinitesimals permits a radically simplified approach to stochastic calculus
  • Chapters on asset pricing, Lévy processes and the Feynman path integral introduce readers to applications
  • Appendixes explore the relationship with Internal Set Theory and Robinsonian nonstandard analysis
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  • ISBN 978-3-642-33149-7
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About this book

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.

Table of contents (10 chapters)

  • Infinitesimal Calculus, Consistently and Accessibly

    Herzberg, Frederik S.

    Pages 1-5

  • Radically Elementary Probability Theory

    Herzberg, Frederik S.

    Pages 7-17

  • Radically Elementary Stochastic Integrals

    Herzberg, Frederik S.

    Pages 19-34

  • The Radically Elementary Girsanov Theorem and the Diffusion Invariance Principle

    Herzberg, Frederik S.

    Pages 35-44

  • Excursion to Financial Economics: A Radically Elementary Approach to the Fundamental Theorems of Asset Pricing

    Herzberg, Frederik S.

    Pages 45-53

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-33149-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-33148-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Calculus with Infinitesimals
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2067
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-33149-7
DOI
10.1007/978-3-642-33149-7
Softcover ISBN
978-3-642-33148-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVIII, 112
Topics