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Symbolic Itô calculus in AXIOM: An ongoing story

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Abstract

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.

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  1. Department of Statistics, University of Warwick, Coventry, CV4 7AL, West Midlands, United Kingdom

    Wilfrid S. Kendall

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Kendall, W.S. Symbolic Itô calculus in AXIOM: An ongoing story. Statistics and Computing 11, 25–35 (2001). https://doi.org/10.1023/A:1026553731272

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