Random and Quasi-Random Point Sets PDF
Edited by Peter Hellekalek, Gerhard Larcher
Part of the Lecture Notes in Statistics series
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Description
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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Download Now
- Format:PDF
- Publisher:Springer New York
- Publication Date:06/12/2012
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- ISBN:9781461217022
Information
-
Download Now
- Format:PDF
- Publisher:Springer New York
- Publication Date:06/12/2012
- Category:
- ISBN:9781461217022