Asymptotic Approximations for Probability Integrals

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Publisher : Springer
ISBN 13 : 3540490337
Total Pages : 157 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Asymptotic Approximations for Probability Integrals by : Karl W. Breitung

Download or read book Asymptotic Approximations for Probability Integrals written by Karl W. Breitung and published by Springer. This book was released on 2006-11-14 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : Springer Verlag
ISBN 13 : 9780387586175
Total Pages : 146 pages
Book Rating : 4.5/5 (861 download)

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Book Synopsis Asymptotic Approximations for Probability Integrals by : Karl Wilhelm Breitung

Download or read book Asymptotic Approximations for Probability Integrals written by Karl Wilhelm Breitung and published by Springer Verlag. This book was released on 1994-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : Academic Press
ISBN 13 : 1483220710
Total Pages : 561 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Asymptotic Approximations of Integrals by : R. Wong

Download or read book Asymptotic Approximations of Integrals written by R. Wong and published by Academic Press. This book was released on 2014-05-10 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotic Approximations for Probability Integrals

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Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (75 download)

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Book Synopsis Asymptotic Approximations for Probability Integrals by : Karl Breitung

Download or read book Asymptotic Approximations for Probability Integrals written by Karl Breitung and published by . This book was released on 1989 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotic Approximations of Integrals

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Publisher :
ISBN 13 :
Total Pages : 543 pages
Book Rating : 4.:/5 (933 download)

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Book Synopsis Asymptotic Approximations of Integrals by :

Download or read book Asymptotic Approximations of Integrals written by and published by . This book was released on 2001 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotic Approximations of Integrals

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Publisher : Boston [Mass.] ; Toronto : Academic Press
ISBN 13 : 9780127625355
Total Pages : 544 pages
Book Rating : 4.6/5 (253 download)

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Book Synopsis Asymptotic Approximations of Integrals by : Roderick Wong

Download or read book Asymptotic Approximations of Integrals written by Roderick Wong and published by Boston [Mass.] ; Toronto : Academic Press. This book was released on 1989 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotic Expansions of Integrals

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Publisher : Courier Corporation
ISBN 13 : 0486650820
Total Pages : 453 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Asymptotic Expansions of Integrals by : Norman Bleistein

Download or read book Asymptotic Expansions of Integrals written by Norman Bleistein and published by Courier Corporation. This book was released on 1986-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Normal Approximation and Asymptotic Expansions

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Publisher : SIAM
ISBN 13 : 089871897X
Total Pages : 333 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Normal Approximation and Asymptotic Expansions by : Rabi N. Bhattacharya

Download or read book Normal Approximation and Asymptotic Expansions written by Rabi N. Bhattacharya and published by SIAM. This book was released on 2010-11-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: -Fourier analysis, --

Asymptotic Methods For Integrals

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Publisher : World Scientific
ISBN 13 : 9814612170
Total Pages : 628 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Asymptotic Methods For Integrals by : Nico M Temme

Download or read book Asymptotic Methods For Integrals written by Nico M Temme and published by World Scientific. This book was released on 2014-10-31 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Approximation, Probability, and Related Fields

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Publisher : Springer Science & Business Media
ISBN 13 : 1461524946
Total Pages : 441 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Approximation, Probability, and Related Fields by : George A. Anastassiou

Download or read book Approximation, Probability, and Related Fields written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a conference held in Santa Barbara, California, May 20-22, 1993

Asymptotic Methods for Integrals

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Publisher : World Scientific Publishing Company
ISBN 13 : 9789814612159
Total Pages : 0 pages
Book Rating : 4.6/5 (121 download)

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Book Synopsis Asymptotic Methods for Integrals by : Nico M. Temme

Download or read book Asymptotic Methods for Integrals written by Nico M. Temme and published by World Scientific Publishing Company. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotic Approximations of Integrals with Applications

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Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (122 download)

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Book Synopsis Asymptotic Approximations of Integrals with Applications by :

Download or read book Asymptotic Approximations of Integrals with Applications written by and published by . This book was released on 2020 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis analyzes asymptotic approximations expansions for integrals, with several examples given. The main part of this research consists in studying the function g(x) = (1 + 1=x)x, which has the limit e as x → ∞. In a 2014 paper C.-P. Chen and J. Choi previously studied this function through an asymptotic expansion for large x. Our main focus is on the coefficients that appear in their expansion. Chen and Choi obtained an explicit formula for the coefficients, but it involves a sum of terms that grows exponentially in number. Our contribution is to find the coefficients in a more practical way, and also to determine the asymptotic behavior of the nth term as n → ∞. We derive a recursion formula, and we show it is simple to use and is numerically stable. We then use Cauchy’s integral formula to derive an explicit integral representation for the coefficients. From this we approximate the late coefficients by residue theory, and this approximation consists of two simple terms. We show the accuracy of the approximation with some numerical examples. We finally determine an integral representation of the error term in our asymptotic approximation, and from this show that is of smaller order of magnitude than the two leading terms.

Approximating Integrals via Monte Carlo and Deterministic Methods

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Publisher : OUP Oxford
ISBN 13 : 019158987X
Total Pages : 302 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Approximating Integrals via Monte Carlo and Deterministic Methods by : Michael Evans

Download or read book Approximating Integrals via Monte Carlo and Deterministic Methods written by Michael Evans and published by OUP Oxford. This book was released on 2000-03-23 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.

Asymptotic Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 1468400290
Total Pages : 266 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Asymptotic Analysis by : Ricardo Estrada

Download or read book Asymptotic Analysis written by Ricardo Estrada and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro vide a systematic procedure to assign values to the divergent integrals that often appear in the literature.

Reliability and Optimization of Structural Systems ’88

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Publisher : Springer Science & Business Media
ISBN 13 : 3642838286
Total Pages : 432 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Reliability and Optimization of Structural Systems ’88 by : P. Thoft-Christensen

Download or read book Reliability and Optimization of Structural Systems ’88 written by P. Thoft-Christensen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Analysis

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Publisher : Birkhauser
ISBN 13 : 9781468400311
Total Pages : 268 pages
Book Rating : 4.4/5 (3 download)

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Book Synopsis Asymptotic Analysis by : Ricardo Estrada

Download or read book Asymptotic Analysis written by Ricardo Estrada and published by Birkhauser. This book was released on 2012 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 Basic Results in Asymptotics.- 1.1 Introduction.- 1.2 Order Symbols.- 1.3 Asymptotic Series.- 1.4 Algebraic and Analytic Operations.- 1.5 Existence of Functions with a Given Asymptotic Expansion.- 1.6 Asymptotic Power Series in a Complex Variable.- 1.7 Asymptotic Approximation of Partial Sums.- 1.8 The Euler-Maclaurin Summation Formula.- 2 Introduction to the Theory of Distributions.- 2.1 Introduction.- 2.2 The Space of Distributions $$\mathcal{D}'$$.- 2.3 Algebraic and Analytic Operations.- 2.4 Regularization, Pseudofunction and Hadamard Finite Part.- 2.5 Support and Order.- 2.6 Homogeneous Distributions.- 2.7 Distributional Derivatives of Discontinuous Functions.- 2.8 Tempered Distributions and the Fourier Transform.- 2.9 Distributions of Rapid Decay.- 2.10 Spaces of Distributions Associated with an Asymptotic Sequence.- 3 A Distributional Theory of Asymptotic Expansions.- 3.1 Introduction.- 3.2 The Taylor Expansion of Distributions.- 3.3 The Moment Asymptotic Expansion.- 3.4 Expansions in the Space $$\mathcal{P}'$$.- 3.5 Laplace's Asymptotic Formula.- 3.6 The Method of Steepest Descent.- 3.7 Expansion of Oscillatory Kernels.- 3.8 The Expansion of f(?x) as ? -> ? in Other Cases.- 3.9 Asymptotic Separation of Variables.- 4 The Asymptotic Expansion of Multidimensional Generalized Functions.- 4.1 Introduction.- 4.2 Taylor Expansion in Several Variables.- 4.3 The Multidimensional Moment Asymptotic Expansion.- 4.4 Laplace's Formula.- 4.5 Fourier Type Integrals.- 4.6 Further Examples.- 4.7 Tensor Products and Partial Asymptotic Expansions.- 4.8 An Application in Quantum Mechanics.- 5 The Asymptotic Expansion of Certain Series Considered by Ramanujan.- 5.1 Introduction.- 5.2 Basic Formulas.- 5.3 Lambert Type Series.- 5.4 Distributionally Small Sequences.- 5.5 Multiple Series.- 6 Series of Dirac Delta Functions.- 6.1 Introduction.- 6.2 Basic Notions.- 6.3 Several Problems That Lead to Series of Deltas.- 6.4 Dual Taylor Series as Asymptotics of Solutions of Differential Equations.- 6.5 Singular Perturbations.- References.

Asymptotic Approximation of Integrals

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Publisher :
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.:/5 (192 download)

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Book Synopsis Asymptotic Approximation of Integrals by : Roderick Wong

Download or read book Asymptotic Approximation of Integrals written by Roderick Wong and published by . This book was released on 1989 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: