Summary
It has been proposed by Owen et al. [CMO97,LO02] that the surprising efficacy of quasi-Monte Carlo methods, when applied to certain high-dimensional integrands arising in mathematical finance, results from the integrands being effectively low-dimensional in the superposition sense. In this paper, mathematical results are presented which relate effective low-dimensionality with the structure of the underlying stochastic differential equation.
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Dickinson, A. (2006). Explaining Effective Low-Dimensionality. In: Niederreiter, H., Talay, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31186-6_7
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DOI: https://doi.org/10.1007/3-540-31186-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25541-3
Online ISBN: 978-3-540-31186-7
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