Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality

Christoph Aistleitner, and Josef Dick. "Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality." Acta Arithmetica 167.2 (2015): 143-171. <http://eudml.org/doc/279219>.

@article{ChristophAistleitner2015,
abstract = {We prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma-Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. We also discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure into a sequence with low discrepancy with respect to a general measure μ, and show the limitations of a method suggested by Chelson.},
author = {Christoph Aistleitner, Josef Dick},
journal = {Acta Arithmetica},
keywords = {function of bounded variation; numerical integration; discrepancy theory; Borel measure},
language = {eng},
number = {2},
pages = {143-171},
title = {Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality},
url = {http://eudml.org/doc/279219},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Christoph Aistleitner
AU - Josef Dick
TI - Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 2
SP - 143
EP - 171
AB - We prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma-Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. We also discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure into a sequence with low discrepancy with respect to a general measure μ, and show the limitations of a method suggested by Chelson.
LA - eng
KW - function of bounded variation; numerical integration; discrepancy theory; Borel measure
UR - http://eudml.org/doc/279219
ER -