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A distributed procedure for computing stochastic expansions with Mathematica
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Ladroue, Christophe and Papavasiliou, Anastasia (2013) A distributed procedure for computing stochastic expansions with Mathematica. Journal of Statistical Software, Volume 53 (Number 11). ISSN 1548-7660.
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Official URL: http://www.jstatsoft.org/v53/i11
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.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Statistics |
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| Library of Congress Subject Headings (LCSH): | Stochastic processes, Multiple integrals, Probabilities, Mathematica (Computer file) | ||||
| Journal or Publication Title: | Journal of Statistical Software | ||||
| Publisher: | University of California, Los Angeles | ||||
| ISSN: | 1548-7660 | ||||
| Official Date: | May 2013 | ||||
| Dates: |
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| Volume: | Volume 53 | ||||
| Number: | Number 11 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Date of first compliant deposit: | 25 December 2015 | ||||
| Date of first compliant Open Access: | 25 December 2015 | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
| Grant number: | EP/H019588/1 (EPSRC) |
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