Given a finite sequence U_N={u_1,…,u_N} of points contained in the d-dimensional unit torus, we consider the L^2 discrepancy between the integral of a given function and the Riemann sums with respect to translations of U_N. We show that with positive probability, the L^2 discrepancy of other sequences close to U_N in a certain sense preserves the order of decay of the discrepancy of U_N. We also study the role of the regularity of the given function.

Brandolini, L., Chen, W., Gigante, G., & Travaglini, G. (2009). Discrepancy for randomized Riemann sums. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 137, 3177-3185.

Discrepancy for randomized riemann sums

TRAVAGLINI, GIANCARLO
2009

Abstract

Given a finite sequence U_N={u_1,…,u_N} of points contained in the d-dimensional unit torus, we consider the L^2 discrepancy between the integral of a given function and the Riemann sums with respect to translations of U_N. We show that with positive probability, the L^2 discrepancy of other sequences close to U_N in a certain sense preserves the order of decay of the discrepancy of U_N. We also study the role of the regularity of the given function.
Articolo in rivista - Articolo scientifico
Riemann sums; discrepancy; Fourier Analysis
English
Brandolini, L., Chen, W., Gigante, G., & Travaglini, G. (2009). Discrepancy for randomized Riemann sums. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 137, 3177-3185.
Brandolini, L; Chen, W; Gigante, G; Travaglini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/6074
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