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Random cubatures and quasi-Monte Carlo methods

Author

Listed:
  • 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)

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.

Suggested Citation

  • Antonov Anton A. & Ermakov Sergej M., 2015. "Random cubatures and quasi-Monte Carlo methods," Monte Carlo Methods and Applications, De Gruyter, vol. 21(3), pages 179-187, September.
    • Handle: RePEc:bpj:mcmeap:v:21:y:2015:i:3:p:179-187:n:2
    DOI: 10.1515/mcma-2015-0102
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