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A Distributed Procedure for Computing Stochastic Expansions with Mathematica

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  • Ladroue, Christophe
  • Papavaviliou, Anastasia

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.

Suggested Citation

  • Ladroue, Christophe & Papavaviliou, Anastasia, 2013. "A Distributed Procedure for Computing Stochastic Expansions with Mathematica," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i11).
    • Handle: RePEc:jss:jstsof:v:053:i11
    DOI: http://hdl.handle.net/10.18637/jss.v053.i11
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    Cited by:

    1. Chenxu Li & Yu An & Dachuan Chen & Qi Lin & Nian Si, 2016. "Efficient computation of the likelihood expansions for diffusion models," IISE Transactions, Taylor & Francis Journals, vol. 48(12), pages 1156-1171, December.

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