Statistics and Computing

, Volume 11, Issue 1, pp 25–35

Symbolic Itô calculus in AXIOM: An ongoing story

  • Wilfrid S. Kendall

DOI: 10.1023/A:1026553731272

Cite this article as:
Kendall, W.S. Statistics and Computing (2001) 11: 25. doi:10.1023/A:1026553731272


Symbolic Itô calculus refers both to the implementation of Itô calculus in a computer algebra package and to its application. This article reports on progress in the implementation of Itô calculus in the powerful and innovative computer algebra package AXIOM, in the context of a decade of previous implementations and applications. It is shown how the elegant algebraic structure underlying the expressive and effective formalism of Itô calculus can be implemented directly in AXIOM using the package's programmable facilities for “strong typing” of computational objects. An application is given of the use of the implementation to provide calculations for a new proof, based on stochastic differentials, of the Mardia-Dryden distribution from statistical shape theory.

AXIOM computer algebra coupling of random processes financial mathematics Itô formula Itô calculus Itovsn3 Mardia-Dryden density Mathematica Macsyma Maple REDUCE semimartingale statistics of shape stochastic calculus stochastic integral symbolic Itô calculus 

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Wilfrid S. Kendall
    • 1
  1. 1.Department of StatisticsUniversity of Warwick, CoventryWest MidlandsUnited Kingdom

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