Random and Quasi-Random Point Sets

Language: English

Published by Springer New York, 1998

0387985549 / 9780387985541

Series: Book 12 of 72 - Lecture Notes in Statistics

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Zustand: Sehr gut | Seiten: 348 | Sprache: Englisch | Produktart: Bücher | 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.

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Title
Random and Quasi-Random Point Sets
Author
Unbekannt
Publisher
Springer New York
Publication year
1998
Condition
Sehr gut
Binding
Soft cover
Language
English
ISBN 10
0387985549
ISBN 13
9780387985541
Series
Book 12 of 72: Lecture Notes in Statistics
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