Random and Quasi-Random Point Sets

Peter Hellekalek, Gerhard Larcher, J. Beck, P. Hellekalek, P. Hickernell, G. Larcher, P. L'Ecuyer, H. Niederreiter, S. Tezuka et C. Xing

ISBN 10: 0387985549 / ISBN 13: 9780387985541

Published by Springer-Verlag New York Inc., 1998

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Ancien livre de bibliothèque. Légères traces d'usure sur la couverture. Edition 1998. Ammareal reverse jusqu'à 15% du prix net de cet article à des organisations caritatives. ENGLISH DESCRIPTION Book Condition: Used, Good. Former library book. Slight signs of wear on the cover. Edition 1998. Ammareal gives back up to 15% of this item's net price to charity organizations.

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Bibliographic Details

• Title: Random and Quasi-Random Point Sets
• Publisher: Springer-Verlag New York Inc.
• Publication Date: 1998
• Language: English
• ISBN 10: 0387985549
• ISBN 13: 9780387985541
• Binding: Softcover
• Condition: Bon

About this title

Synopsis

This volume is a collection of survey papers on recent developments in the fields of quasi-Monte Carlo methods and uniform random number generation. We will cover a broad spectrum of questions, from advanced metric number theory to pricing financial derivatives. The Monte Carlo method is one of the most important tools of system modeling. Deterministic algorithms, so-called uniform random number gen­ erators, are used to produce the input for the model systems on computers. Such generators are assessed by theoretical ("a priori") and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional "random" point sets. The degree of uniformity is strongly related to the degree of correlations within the random numbers. The quasi-Monte Carlo approach aims at improving the rate of conver­ gence in the Monte Carlo method by number-theoretic techniques. It yields deterministic bounds for the approximation error. The main mathematical tool here are so-called low-discrepancy sequences. These "quasi-random" points are produced by deterministic algorithms and should be as "super"­ uniformly distributed as possible. Hence, both in uniform random number generation and in quasi-Monte Carlo methods, we study the uniformity of deterministically generated point sets in high dimensions. By a (common) abuse oflanguage, one speaks of random and quasi-random point sets. The central questions treated in this book are (i) how to generate, (ii) how to analyze, and (iii) how to apply such high-dimensional point sets.