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Engineering - Computational Intelligence and Complexity | Asymptotic Approximations for Probability Integrals

Asymptotic Approximations for Probability Integrals

Series: Lecture Notes in Mathematics, Vol. 1592

Breitung, Karl W.

1994, X, 154 p.

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  • 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.

Content Level » Research

Keywords » Asymptotic approximation - Extreme Values - Gaussian distribution - Laplace method - Normal distribution - geometry - statistics

Related subjects » Computational Intelligence and Complexity - Geometry & Topology - Probability Theory and Stochastic Processes - Theoretical, Mathematical & Computational Physics

Table of contents 

Mathematical preliminaries.- Asymptotic analysis.- Univariate integrals.- Multivariate laplace type integrals.- Approximations for normal integrals.- Arbitrary probability integrals.- Crossing rates of stochastic processes.

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