Random Number Generation and Quasi-Monte Carlo Methods
Title | Random Number Generation and Quasi-Monte Carlo Methods PDF eBook |
Author | Harald Niederreiter |
Publisher | SIAM |
Pages | 243 |
Release | 1992-01-01 |
Genre | Mathematics |
ISBN | 0898712955 |
This volume contains recent work in uniform pseudorandom number generation and quasi-Monte Carlo methods, and stresses the interplay between them.
Random Number Generation and Monte Carlo Methods
Title | Random Number Generation and Monte Carlo Methods PDF eBook |
Author | James E. Gentle |
Publisher | Springer Science & Business Media |
Pages | 252 |
Release | 2013-03-14 |
Genre | Computers |
ISBN | 147572960X |
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.
Random and Quasi-Random Point Sets
Title | Random and Quasi-Random Point Sets PDF eBook |
Author | Peter Hellekalek |
Publisher | Springer |
Pages | 0 |
Release | 1998-10-09 |
Genre | Mathematics |
ISBN | 9780387985541 |
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.
Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
Title | Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing PDF eBook |
Author | Harald Niederreiter |
Publisher | Springer Science & Business Media |
Pages | 391 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461225523 |
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 Sampling
Title | Monte Carlo and Quasi-Monte Carlo Sampling PDF eBook |
Author | Christiane Lemieux |
Publisher | Springer Science & Business Media |
Pages | 373 |
Release | 2009-04-03 |
Genre | Mathematics |
ISBN | 038778165X |
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
Title | Monte Carlo and Quasi-Monte Carlo Methods 1996 PDF eBook |
Author | Harald Niederreiter |
Publisher | Springer Science & Business Media |
Pages | 463 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461216907 |
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.
Modeling Uncertainty
Title | Modeling Uncertainty PDF eBook |
Author | Moshe Dror |
Publisher | Springer Science & Business Media |
Pages | 810 |
Release | 2002-01-31 |
Genre | Business & Economics |
ISBN | 9780792374633 |
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.