Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
Authors: Christophe Ladroue, Anastasia Papavaviliou
Title: A Distributed Procedure for Computing Stochastic Expansions with Mathematica
Abstract: The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of the drivers and can be calculated using Picard Iterations. However, such expansions grow exponentially fast in their number of terms, due to their specific algebra, rendering their practical use limited.

We present a Mathematica procedure that addresses this issue by reparametrizing the polynomials and distributing the load in as small as possible parts that can be processed and manipulated independently, thus alleviating large memory requirements and being perfectly suited for parallelized computation. We also present an iterative implementation of the shuffle product (as opposed to a recursive one, more usually implemented) as well as a fast way for calculating the expectation of iterated Stratonovich integrals for Brownian motion.

Page views:: 1669. Submitted: 2010-08-25. Published: 2013-05-29.
Paper: A Distributed Procedure for Computing Stochastic Expansions with Mathematica     Download PDF (Downloads: 1479)
DistributedExpansion.m: Mathematica source package Download (Downloads: 378; 11KB)
DistributedExpansion.nb: Mathematica notebook for tests and step-by-step examples Download (Downloads: 386; 77KB)

DOI: 10.18637/jss.v053.i11

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Paper: Creative Commons Attribution 3.0 Unported License
Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license.