Asymptotic Approximations for Probability Integrals

Karl Wilhelm Breitung (auth.)3540586172, 9783540586173, 0387586172

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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Table of contents :
Introduction….Pages 1-8
Mathematical preliminaries….Pages 9-33
Asymptotic analysis….Pages 34-44
Univariate integrals….Pages 45-50
Multivariate laplace type integrals….Pages 51-84
Approximations for normal integrals….Pages 85-105
Arbitrary probability integrals….Pages 106-120
Crossing rates of stochastic processes….Pages 121-134