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Abstract
We establish and examine the deep connection between highly stratified random cubature formulas and quasi-Monte Carlo methods. A class of such formulas, designed to exactly integrate the introduced generalized s-dimensional Haar system, is shown to have additional variance reduction compared to the known theoretical upper bound. We propose several equivalent expressions for the variance within the standard quasi-Monte Carlo setting. The theory of random cubatures is supplemented with both refined versions of known results and completely new facts.
Keywords: Monte Carlo; quasi-Monte Carlo; high-dimensional integration; stratified sampling; random cubature formulas; Sobol sequences
Funding source: RFBR
Award Identifier / Grant number: 14-01-00271
Received: 2015-2-24
Accepted: 2015-4-24
Published Online: 2015-5-5
Published in Print: 2015-9-1
© 2015 by De Gruyter
