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The effective dimension and quasi-Monte Carlo integration. (English) Zbl 1021.65002

It was found empirically that quasi-Monte Carlo methods are superior to Monte Carlo methods for high-dimensional integrals arising in finance. This performance is related the notion of effective dimension. The main objectives of this paper are: (1) to analyse the effective dimension for some functions; (2) to develop numerical algorithms for determining the effective dimension of an arbitrary square integrable function; (3) to compare the performance of dimension reduction techniques.

MSC:

65C05 Monte Carlo methods
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