Digital Nets and Sequences

Digital Nets and Sequences PDF

Author: Josef Dick

Publisher: Cambridge University Press

Published: 2010-09-09

Total Pages: 619

ISBN-13: 1139490052

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Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.

Digital Nets and Sequences

Digital Nets and Sequences PDF

Author: Josef Dick

Publisher:

Published: 2014-05-14

Total Pages: 620

ISBN-13: 9780511901973

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An introduction to contemporary quasi Monte Carlo methods, digital nets and sequences, and discrepancy theory. Includes many exercises, examples and illustrations.

Monte Carlo and Quasi-Monte Carlo Methods 2008

Monte Carlo and Quasi-Monte Carlo Methods 2008 PDF

Author: Pierre L' Ecuyer

Publisher: Springer Science & Business Media

Published: 2010-01-14

Total Pages: 669

ISBN-13: 3642041078

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This book represents the refereed proceedings of the Eighth International Conference on Monte Carlo (MC)and Quasi-Monte Carlo (QMC) Methods in Scientific Computing, held in Montreal (Canada) in July 2008. It covers the latest theoretical developments as well as important applications of these methods in different areas. It contains two tutorials, eight invited articles, and 32 carefully selected articles based on the 135 contributed presentations made at the conference. This conference is a major event in Monte Carlo methods and is the premiere event for quasi-Monte Carlo and its combination with Monte Carlo. This series of proceedings volumes is the primary outlet for quasi-Monte Carlo research.

Parallel and Distributed Processing and Applications

Parallel and Distributed Processing and Applications PDF

Author: Jiannong Cao

Publisher: Springer

Published: 2005-01-17

Total Pages: 1080

ISBN-13: 3540305661

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Welcometotheproceedingsofthe2ndInternationalSymposiumonParalleland Distributed Processing and Applications (ISPA2004) which was held in Hong Kong, China, 13–15 December, 2004. With the advance of computer networks and hardware technology, parallel and distributed processing has become a key technology which plays an imp- tant part in determining future research and development activities in many academic and industrial branches. It provides a means to solve computati- ally intensive problems by improving processing speed. It is also the only - ableapproachtobuildinghighlyreliableandinherentlydistributedapplications. ISPA2004 provided a forum for scientists and engineers in academia and ind- try to exchange and discuss their experiences, new ideas, research results, and applications about all aspects of parallel and distributed computing. There was a very large number of paper submissions (361) from 26 countries and regions, including not only Asia and the Paci?c, but also Europe and North America. All submissions were reviewed by at least three program or technical committee members or external reviewers. It was extremely di?cult to select the presentations for the conference because there were so many excellent and interesting submissions. In order to allocate as many papers as possible and keep the high quality of the conference, we ?nally decided to accept 78 regular papers and 38 short papers for oral technical presentations. We believe that all of these papers and topics not only provide novel ideas, new results, work in progress and state-of-the-art techniques in this ?eld, but also stimulate the future research activities in the area of parallel and distributed computing with applications.

Monte Carlo and Quasi-Monte Carlo Methods

Monte Carlo and Quasi-Monte Carlo Methods PDF

Author: Bruno Tuffin

Publisher: Springer Nature

Published: 2020-05-01

Total Pages: 533

ISBN-13: 3030434656

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​This book presents the refereed proceedings of the 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Rennes, France, and organized by Inria, in July 2018. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.

Discrepancy Theory

Discrepancy Theory PDF

Author: Dmitriy Bilyk

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-01-20

Total Pages: 303

ISBN-13: 3110651203

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The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory

Monte Carlo and Quasi-Monte Carlo Sampling

Monte Carlo and Quasi-Monte Carlo Sampling PDF

Author: Christiane Lemieux

Publisher: Springer Science & Business Media

Published: 2009-04-03

Total Pages: 373

ISBN-13: 038778165X

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Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods.

Random and Quasi-Random Point Sets

Random and Quasi-Random Point Sets PDF

Author: Peter Hellekalek

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 345

ISBN-13: 1461217024

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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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