Symbolic Itô Calculus.
Symbolic Itô Calculus is the name for my implementation of
Itô calculus (stochastic calculus for continuous semimartingales)
in various computer algebra packages. See below for various Warwick Statistics
Department preprints describing aspects of the work. If you want to get
hold of the software then there are various possibilities depending on
what is your favourite computer algebra package.
The other preprints describe various applications; their inspection would
give an idea of the possibilities. You can read
abstracts of my other papers (and some
links to downloadable preprints) here. Preprint 247 is the text of a computer-illustrated talk I can give
about Brownian motion, which in part provides a brief and elementary introduction
to symbolic Itô calculus. Contact me at W.S.Kendall@warwick.ac.uk
if you want to find out more about this.
If you want copies of any of these reports then please mail or fax your
requests to the departmental secretary at the address below, or use email:
161: The Euclidean diffusion of shape [Abstract].
202: A remark on the proof of Itô's formula for C2 functions of continuous
203: Computer algebra and stochastic calculus [Abstract].
217: Symbolic Itô calculus: an introduction [Abstract].
222: (with O.E. Barndorff-Nielsen and P.E. Jupp) Stochastic calculus,
statistical asymptotics, Taylor strings and phyla [Abstract].
223: Symbolic Itô calculus: an overview [Abstract].
236: Computer algebra in probability and statistics [Abstract].
237: Computer algebra and yoke geometry I: When is an expression a tensor?
238: Itovsn3: doing stochastic calculus with Mathematica
247: Brownian motion and computer algebra (Text of talk to BAAS Science
Festival '92, Southampton Wednesday 26 August 1992, with screenshots of
illustrative animations) [Abstract].
261: (with G. Ben Arous and M. Cranston) Coupling constructions
for hypoelliptic diffusions: Two examples [Abstract].
296: A diffusion model for Bookstein triangle shape [Abstract]:
[Gzipped Postscript Paper: 67k].
301: Computer algebra: an article for the Wiley Encyclopaedia of Biostatistics.
327: Symbolic Itô calculus in AXIOM: an ongoing story. [Abstract]:
[Gzipped Postscript Paper: 112k] (describes
the new AXIOM implementation).
328: Itovsn3 in AXIOM: modules, algebras, and stochastic
differentials. [Abstract]: [Gzipped
Postscript Paper: 152k] (presents details of the new AXIOM implementation).
331: (with K. Burdzy): Efficient Markovian couplings: examples and
counterexamples. [Abstract]: [Gzipped
Postscript Paper: 224k] (includes incidental application to reflected
Brownian motion in a wedge).
333: Stochastic calculus in Mathematica: software and examples.
[Abstract] (a slightly updated implementation
of the Mathematica version as described in Preprint 238, with a
number of extra applications in Mathematica notebook form).
Department of Statistics,
University of Warwick,
Coventry CV4 7AL, UK
Tel: +44 2476 523066
Fax: +44 2476 524532
Version: $State: W95 $ $Revision: 1.1 $
Last update: $Date: 1999/07/31 18:45:52 $