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  • © 2013

Stochastic Calculus with Infinitesimals

Authors:

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2067)

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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.

Authors and Affiliations

  • Institute of Mathematical Economics, Bielefeld University, Bielefeld, Germany

    Frederik Herzberg

Bibliographic Information

Buy it now

Buying options

eBook USD 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access