The effective dimension and quasi-Monte Carlo integration
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.
scientific article; zbMATH DE number 1903487
scientific article