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

• Autorzy: Christoph Aistleitner , Josef Dick
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11K38: Irregularities of distribution, discrepancy
• 65C05: Monte Carlo methods
• 26B30: Absolutely continuous functions, functions of bounded variation
• 65D30: Numerical integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 2
• Strony: 143-171

Daty

wydano

2015

Twórcy

autor

Christoph Aistleitner

• Department of Mathematics and Statistics, Graduate School of Science, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan

autor

Josef Dick

• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

Identyfikatory

DOI

10.4064/aa167-2-4