Random cubatures and quasi-Monte Carlo methods

Antonov Anton A. () and Ermakov Sergej M. ()
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Antonov Anton A.: Saint Petersburg State University 7–9, Universitetskaya nab., 199034, St.Petersburg, Russia
Ermakov Sergej M.: Saint Petersburg State University 7–9, Universitetskaya nab., 199034, St.Petersburg, Russia

Monte Carlo Methods and Applications, 2015, vol. 21, issue 3, 179-187

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 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/mcma-2015-0102

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