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Asymptotic Approximations for Probability Integrals

  • Book
  • © 1994

Overview

Authors:
  1. Karl Wilhelm Breitung
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1592)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Karl Wilhelm Breitung
    Pages 1-8

  3. Mathematical preliminaries

    • Karl Wilhelm Breitung
    Pages 9-33

  4. Asymptotic analysis

    • Karl Wilhelm Breitung
    Pages 34-44

  5. Univariate integrals

    • Karl Wilhelm Breitung
    Pages 45-50

  6. Multivariate laplace type integrals

    • Karl Wilhelm Breitung
    Pages 51-84

  7. Approximations for normal integrals

    • Karl Wilhelm Breitung
    Pages 85-105

  8. Arbitrary probability integrals

    • Karl Wilhelm Breitung
    Pages 106-120

  9. Crossing rates of stochastic processes

    • Karl Wilhelm Breitung
    Pages 121-134

  10. Back Matter

    Pages 135-149
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Keywords

About this book

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.

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