TY - JOUR

T1 - Discrepancy for randomized riemann sums

AU - Brandolini, Luca

AU - Chen, William

AU - Gigante, Giacomo

AU - Travaglini, Giancarlo

N1 - Copyright 2009 American Mathematical Society. First published in Proceedings of the American Mathematical Society, Volume 137, Issue 10, pp. 3187-3196, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0002-9939-09-09975-4.

PY - 2009/10

Y1 - 2009/10

N2 - Given a finite sequence UN = {u1,., uN} of points contained in the d-dimensional unit torus, we consider the L2 discrepancy between the integral of a given function and the Riemann sums with respect to translations of UN. We show that with positive probability, the L2 discrepancy of other sequences close to UN in a certain sense preserves the order of decay of the discrepancy of UN. We also study the role of the regularity of the given function.

AB - Given a finite sequence UN = {u1,., uN} of points contained in the d-dimensional unit torus, we consider the L2 discrepancy between the integral of a given function and the Riemann sums with respect to translations of UN. We show that with positive probability, the L2 discrepancy of other sequences close to UN in a certain sense preserves the order of decay of the discrepancy of UN. We also study the role of the regularity of the given function.

UR - http://www.scopus.com/inward/record.url?scp=77951049048&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-09-09975-4

DO - 10.1090/S0002-9939-09-09975-4

M3 - Article

AN - SCOPUS:77951049048

VL - 137

SP - 3187

EP - 3196

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -