Asymptotic Approximations for Probability Integrals

Asymptotic Approximations for Probability Integrals

Author: Karl W. Breitung

Publisher: Springer

Published: 2006-11-14

Total Pages: 157

ISBN-13: 3540490337

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This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.


Asymptotic Approximations for Probability Integrals

Asymptotic Approximations for Probability Integrals

Author: Karl Wilhelm Breitung

Publisher: Springer Verlag

Published: 1994-01-01

Total Pages: 146

ISBN-13: 9780387586175

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This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.


Asymptotic Approximations of Integrals

Asymptotic Approximations of Integrals

Author: R. Wong

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 561

ISBN-13: 1483220710

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Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.


Reliability and Optimization of Structural Systems ’88

Reliability and Optimization of Structural Systems ’88

Author: P. Thoft-Christensen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 432

ISBN-13: 3642838286

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The present book contains 30 papers presented at the 2nd Working Conference on Reliability and Optimization of Structural Systems. The purpose of the Working Group was - to promote modern structural system optimization and reliability theory, - to advance international cooperation in the field of structural system optimization and reliability theory, - to stimulate research, development and application of structural system optimization and reliability theory, - to further the dissemination and exchange of information on reliability and optimization of structural system optimization and reliability theory, - to encourage education in structural system optimization and reliability theory.


Asymptotic Methods for Integrals

Asymptotic Methods for Integrals

Author: Nico M. Temme

Publisher: World Scientific Publishing Company

Published: 2015

Total Pages: 0

ISBN-13: 9789814612159

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This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.


Reliability and Optimization of Structural Systems

Reliability and Optimization of Structural Systems

Author: Rudiger Rackwitz

Publisher: Springer

Published: 2013-06-05

Total Pages: 321

ISBN-13: 0387348662

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The 6th meeting sponsored by IFIP Working Group 7.5, on reliability and optimization of structural systems, took place in September 1994 in Assisi, Italy. This book contains the papers presented at the working conference including topics such as reliability of special structures, fatigue, failure modes and time-variant systems relibility.


Statistical Methods for QTL Mapping

Statistical Methods for QTL Mapping

Author: Zehua Chen

Publisher: CRC Press

Published: 2013-11-01

Total Pages: 944

ISBN-13: 0415669863

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While numerous advanced statistical approaches have recently been developed for quantitative trait loci (QTL) mapping, the methods are scattered throughout the literature. Statistical Methods for QTL Mapping brings together many recent statistical techniques that address the data complexity of QTL mapping. After introducing basic genetics topics and statistical principles, the author discusses the principles of quantitative genetics, general statistical issues of QTL mapping, commonly used one-dimensional QTL mapping approaches, and multiple interval mapping methods. He then explains how to use a feature selection approach to tackle a QTL mapping problem with dense markers. The book also provides comprehensive coverage of Bayesian models and MCMC algorithms and describes methods for multi-trait QTL mapping and eQTL mapping, including meta-trait methods and multivariate sequential procedures. This book emphasizes the modern statistical methodology for QTL mapping as well as the statistical issues that arise during this process. It gives the necessary biological background for statisticians without training in genetics and, likewise, covers statistical thinking and principles for geneticists. Written primarily for geneticists and statisticians specializing in QTL mapping, the book can also be used as a supplement in graduate courses or for self-study by PhD students working on QTL mapping projects.


The Red Book of Varieties and Schemes

The Red Book of Varieties and Schemes

Author: David Mumford

Publisher: Springer

Published: 2004-02-21

Total Pages: 316

ISBN-13: 3540460217

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Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.


Real Enriques Surfaces

Real Enriques Surfaces

Author: Alexander Degtyarev

Publisher: Springer Science & Business Media

Published: 2000-10-26

Total Pages: 284

ISBN-13: 9783540410881

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Deformation classes. p. 89.


Cellular Spaces, Null Spaces and Homotopy Localization

Cellular Spaces, Null Spaces and Homotopy Localization

Author: Emmanuel Farjoun

Publisher: Springer Science & Business Media

Published: 1996

Total Pages: 220

ISBN-13: 9783540606048

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In this monograph we give an exposition of some recent development in homotopy theory. It relates to advances in periodicity in homotopy localization and in cellular spaces. The notion of homotopy localization is treated quite generally and encompasses all the known idempotent homotopy functors. It is applied to K-theory localizations, to Morava-theories, to Hopkins-Smith theory of types. The method of homotopy colimits is used heavily. It is written with an advanced graduate student in topology and research homotopy theorist in mind.