Monte Carlo And Quasi Monte Carlo Sampling

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Monte Carlo and Quasi-Monte Carlo Sampling

Christiane Lemieux
Monte Carlo and Quasi Monte Carlo Sampling Book PDF

Author : Christiane Lemieux
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 43,5 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.

Monte Carlo and Quasi-Monte Carlo Sampling

Christiane Lemieux
Monte Carlo and Quasi Monte Carlo Sampling Book PDF

Author : Christiane Lemieux
Publisher : Springer
Page : 373 pages
File Size : 45,5 Mb
Release : 2010-11-06
Category : Mathematics
ISBN : 1441926763

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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.

Monte Carlo and Quasi-Monte Carlo Methods 1996

Harald Niederreiter,Peter Hellekalek,Gerhard Larcher,Peter Zinterhof
Monte Carlo and Quasi Monte Carlo Methods 1996 Book PDF

Author : Harald Niederreiter,Peter Hellekalek,Gerhard Larcher,Peter Zinterhof
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461216902

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Monte Carlo and Quasi-Monte Carlo Methods 1996 by Harald Niederreiter,Peter Hellekalek,Gerhard Larcher,Peter Zinterhof Pdf

Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. This volume contains the refereed proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. The conference was a forum for recent progress in the theory and the applications of these methods. The topics covered in this volume range from theoretical issues in Monte Carlo and simulation methods, low-discrepancy point sets and sequences, lattice rules, and pseudorandom number generation to applications such as numerical integration, numerical linear algebra, integral equations, binary search, global optimization, computational physics, mathematical finance, and computer graphics. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods.

Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing

Harald Niederreiter,Peter J. Shiue
Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing Book PDF

Author : Harald Niederreiter,Peter J. Shiue
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 49,7 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.

Monte-Carlo and Quasi-Monte Carlo Methods 1998

Harald Niederreiter,Jerome Spanier
Monte Carlo and Quasi Monte Carlo Methods 1998 Book PDF

Author : Harald Niederreiter,Jerome Spanier
Publisher : Springer
Page : 490 pages
File Size : 48,6 Mb
Release : 2000
Category : Business & Economics
ISBN : STANFORD:36105028525017

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Monte-Carlo and Quasi-Monte Carlo Methods 1998 by Harald Niederreiter,Jerome Spanier Pdf

This book represents the refereed proceedings of the Third International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Claremont Graduate University in 1998. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active area.

Monte Carlo and Quasi-Monte Carlo Methods

Bruno Tuffin,Pierre L'Ecuyer
Monte Carlo and Quasi Monte Carlo Methods Book PDF

Author : Bruno Tuffin,Pierre L'Ecuyer
Publisher : Springer Nature
Page : 533 pages
File Size : 55,8 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.

Random Number Generation and Quasi-Monte Carlo Methods

Harald Niederreiter
Random Number Generation and Quasi Monte Carlo Methods Book PDF

Author : Harald Niederreiter
Publisher : SIAM
Page : 247 pages
File Size : 46,5 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 1611970083

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

Tremendous progress has taken place in the related areas of uniform pseudorandom number generation and quasi-Monte Carlo methods in the last five years. This volume contains recent important work in these two areas, and stresses the interplay between them. Some developments contained here have never before appeared in book form. Includes the discussion of the integrated treatment of pseudorandom numbers and quasi-Monte Carlo methods; the systematic development of the theory of lattice rules and the theory of nets and (t,s)-sequences; the construction of new and better low-discrepancy point sets and sequences; Nonlinear congruential methods; the initiation of a systematic study of methods for pseudorandom vector generation; and shift-register pseudorandom numbers. Based on a series of 10 lectures presented by the author at a CBMS-NSF Regional Conference at the University of Alaska at Fairbanks in 1990 to a selected group of researchers, this volume includes background material to make the information more accessible to nonspecialists.

Introduction to Quasi-Monte Carlo Integration and Applications

Gunther Leobacher,Friedrich Pillichshammer
Introduction to Quasi Monte Carlo Integration and Applications Book PDF

Author : Gunther Leobacher,Friedrich Pillichshammer
Publisher : Springer
Page : 206 pages
File Size : 44,5 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.

Random Number Generation and Quasi-Monte Carlo Methods

Harald Niederreiter
Random Number Generation and Quasi Monte Carlo Methods Book PDF

Author : Harald Niederreiter
Publisher : SIAM
Page : 243 pages
File Size : 54,8 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.

Modeling Uncertainty

Moshe Dror,Pierre Lécuyer,Pierre L'Ecuyer,Ferenc Szidarovszky
Modeling Uncertainty Book PDF

Author : Moshe Dror,Pierre Lécuyer,Pierre L'Ecuyer,Ferenc Szidarovszky
Publisher : Springer Science & Business Media
Page : 810 pages
File Size : 53,9 Mb
Release : 2002-01-31
Category : Business & Economics
ISBN : 0792374630

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Modeling Uncertainty by Moshe Dror,Pierre Lécuyer,Pierre L'Ecuyer,Ferenc Szidarovszky Pdf

Writing in honour of Sid Yakowitz, 50 internationally known scholars have collectively contributed 30 papers on modelling uncertainty to this volume. These include papers with a theoretical emphasis and others that focus on applications.

Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods

Giray Okten
Contributions to the Theory of Monte Carlo and Quasi Monte Carlo Methods Book PDF

Author : Giray Okten
Publisher : Universal-Publishers
Page : 91 pages
File Size : 45,7 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.

Monte Carlo and Quasi-Monte Carlo Methods

Art B. Owen,Peter W. Glynn
Monte Carlo and Quasi Monte Carlo Methods Book PDF

Author : Art B. Owen,Peter W. Glynn
Publisher : Springer
Page : 479 pages
File Size : 53,8 Mb
Release : 2018-07-03
Category : Computers
ISBN : 9783319914367

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Monte Carlo and Quasi-Monte Carlo Methods by Art B. Owen,Peter W. Glynn Pdf

This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. 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, computer graphics and the solution of PDEs.

Monte Carlo and Quasi-Monte Carlo Methods 2004

Harald Niederreiter,Denis Talay
Monte Carlo and Quasi Monte Carlo Methods 2004 Book PDF

Author : Harald Niederreiter,Denis Talay
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 46,5 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9783540311867

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Monte Carlo and Quasi-Monte Carlo Methods 2004 by Harald Niederreiter,Denis Talay Pdf

This book represents the refereed proceedings of the Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and of the Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations. These conferences were held jointly at Juan-les-Pins (France) in June 2004. The proceedings include carefully selected papers on many aspects of Monte Carlo methods, quasi-Monte Carlo methods, and the numerical solution of partial differential equations. The reader will be informed about current research in these very active areas.

Uncertainty in Engineering

Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock
Uncertainty in Engineering Book PDF

Author : Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock
Publisher : Springer Nature
Page : 148 pages
File Size : 45,8 Mb
Release : 2022
Category : Electronic
ISBN : 9783030836405

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Uncertainty in Engineering by Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock Pdf

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.

Applied Number Theory

Harald Niederreiter,Arne Winterhof
Applied Number Theory Book PDF

Author : Harald Niederreiter,Arne Winterhof
Publisher : Springer
Page : 442 pages
File Size : 55,8 Mb
Release : 2015-09-01
Category : Mathematics
ISBN : 9783319223216

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Applied Number Theory by Harald Niederreiter,Arne Winterhof Pdf

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.