Uniform Distribution And Quasi Monte Carlo Methods

Author : Peter Kritzer,Harald Niederreiter,Friedrich Pillichshammer,Arne Winterhof
Publisher : Walter de Gruyter GmbH & Co KG
Page : 294 pages
File Size : 48,9 Mb
Release : 2014-08-19
Category : Mathematics
ISBN : 9783110375039

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Uniform Distribution and Quasi-Monte Carlo Methods by Peter Kritzer,Harald Niederreiter,Friedrich Pillichshammer,Arne Winterhof Pdf

This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.

Author : Harald Niederreiter
Publisher : SIAM
Page : 243 pages
File Size : 53,5 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 9780898712957

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Random Number Generation and Quasi-Monte Carlo Methods by Harald Niederreiter Pdf

This volume contains recent work in uniform pseudorandom number generation and quasi-Monte Carlo methods, and stresses the interplay between them.

Author : Christiane Lemieux
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 52,8 Mb
Release : 2009-04-03
Category : Mathematics
ISBN : 9780387781655

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Monte Carlo and Quasi-Monte Carlo Sampling by Christiane Lemieux Pdf

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.

Author : Giray Okten
Publisher : Universal-Publishers
Page : 91 pages
File Size : 45,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9781581120417

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Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods by Giray Okten Pdf

Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to provide remedies for the disadvantages of quasi-Monte Carlo methods mentioned above. In the first part of the dissertation, a hybrid-Monte Carlo sequence designed to obtain error reduction in high dimensions is studied. Probabilistic results on the discrepancy of this sequence as well as results obtained by applying the sequence to problems from numerical integration and mathematical finance are presented. In the second part of the dissertation, a new hybrid-Monte Carlo method is introduced, in an attempt to obtain a practical statistical error analysis using low-discrepancy sequences. It is applied to problems from mathematical finance and particle transport theory to compare its effectiveness with the conventional methods. In the last part of the dissertation, a generalized quasi-Monte Carlo integration rule is introduced. A Koksma-Hlawka type inequality for the rule is proved, using a new concept for the variation of a function. As a consequence of the rule, error reduction techniques and in particular an "importance sampling" type statement are derived. Problems from different disciplines are used as practical tests for our methods. The numerical results obtained in favor of the methods suggest the practical advantages that can be realized by their use in a wide variety of applications.

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 55,6 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9781475729603

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Random Number Generation and Monte Carlo Methods by James E. Gentle Pdf

Monte Carlo simulation has become one of the most important tools in all fields of science. This book surveys the basic techniques and principles of the subject, as well as general techniques useful in more complicated models and in novel settings. The emphasis throughout is on practical methods that work well in current computing environments.

Author : Gunther Leobacher,Friedrich Pillichshammer
Publisher : Springer
Page : 206 pages
File Size : 45,8 Mb
Release : 2014-09-12
Category : Mathematics
ISBN : 9783319034256

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Introduction to Quasi-Monte Carlo Integration and Applications by Gunther Leobacher,Friedrich Pillichshammer Pdf

This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed explanations comprises, for example, lattice rules, digital nets and sequences and discrepancy theory. It also presents methods currently used in research and discusses practical applications with an emphasis on finance-related problems. Each chapter closes with suggestions for further reading and with exercises which help students to arrive at a deeper understanding of the material presented. The book is based on a one-semester, two-hour undergraduate course and is well-suited for readers with a basic grasp of algebra, calculus, linear algebra and basic probability theory. It provides an accessible introduction for undergraduate students in mathematics or computer science.

Author : Peter Hellekalek,Gerhard Larcher
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217022

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Random and Quasi-Random Point Sets by Peter Hellekalek,Gerhard Larcher Pdf

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.

Author : Bruno Tuffin,Pierre L'Ecuyer
Publisher : Springer Nature
Page : 533 pages
File Size : 40,9 Mb
Release : 2020-05-01
Category : Computers
ISBN : 9783030434656

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Monte Carlo and Quasi-Monte Carlo Methods by Bruno Tuffin,Pierre L'Ecuyer Pdf

​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.

Author : Harald Niederreiter,Peter J. Shiue
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461225522

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Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing by Harald Niederreiter,Peter J. Shiue Pdf

Scientists and engineers are increasingly making use of simulation methods to solve problems which are insoluble by analytical techniques. Monte Carlo methods which make use of probabilistic simulations are frequently used in areas such as numerical integration, complex scheduling, queueing networks, and large-dimensional simulations. This collection of papers arises from a conference held at the University of Nevada, Las Vegas, in 1994. The conference brought together researchers across a range of disciplines whose interests include the theory and application of these methods. This volume provides a timely survey of this field and the new directions in which the field is moving.

Author : Thomas N. Herzog,Graham Lord
Publisher : ACTEX Publications
Page : 276 pages
File Size : 46,6 Mb
Release : 2002
Category : Business & Economics
ISBN : 9781566984331

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Applications of Monte Carlo Methods to Finance and Insurance by Thomas N. Herzog,Graham Lord Pdf

Author : Leszek Plaskota,Henryk Woźniakowski
Publisher : Springer Science & Business Media
Page : 721 pages
File Size : 46,8 Mb
Release : 2012-08-23
Category : Mathematics
ISBN : 9783642274404

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Monte Carlo and Quasi-Monte Carlo Methods 2010 by Leszek Plaskota,Henryk Woźniakowski Pdf

This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. 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. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.

Author : Josef Dick,Friedrich Pillichshammer
Publisher : Cambridge University Press
Page : 619 pages
File Size : 46,7 Mb
Release : 2010-09-09
Category : Computers
ISBN : 9781139490054

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Digital Nets and Sequences by Josef Dick,Friedrich Pillichshammer Pdf

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.

Author : L. Kuipers,H. Niederreiter
Publisher : Courier Corporation
Page : 416 pages
File Size : 47,7 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486149998

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Uniform Distribution of Sequences by L. Kuipers,H. Niederreiter Pdf

The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.

Author : Michael Drmota,Robert F. Tichy
Publisher : Springer
Page : 517 pages
File Size : 54,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540683339

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Sequences, Discrepancies and Applications by Michael Drmota,Robert F. Tichy Pdf

The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.

Author : Peter Hellekalek,Gerhard Larcher
Publisher : Springer
Page : 334 pages
File Size : 53,8 Mb
Release : 1998-10-09
Category : Mathematics
ISBN : 0387985549

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Random and Quasi-Random Point Sets by Peter Hellekalek,Gerhard Larcher Pdf

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.