Random and Quasi-Random Point Sets (eBook)

Gerhard Larcher, Peter Hellekalek (Herausgeber)

eBook Download: PDF

2012
Springer New York (Verlag)
978-1-4612-1702-2 (ISBN)

Infos

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 ("e;a priori"e;) and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional "e;random"e; 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 "e;quasi-random"e; points are produced by deterministic algorithms and should be as "e;super"e;- 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.

Produkt-Details

• Erscheint lt. Verlag: 6.12.2012
• Co-Autor: J. Beck, P. Hellekalek, P. Hickernell, P. L'Ecuyer, G. Larcher, H. Niederreiter, S. Tezuka, C. Xing
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• ISBN-10: 1-4612-1702-4 / 1461217024
• ISBN-13: 978-1-4612-1702-2 / 9781461217022