Asymptotic approximations for probability integrals
By: Karl Wilhelm Breitung.
Contributors: Breitung, Karl Wilhelm, 1953-
Series: Lecture notes in mathematics ;; 1592; Lecture notes in mathematics (Springer-Verlag) ;; 1592.
Publisher: Springer-Verlag
Published: 1994
Place of publication: Berlin; New York
Language: eng
Number of pages: 146
Subjects: Stochastic processes.; Asymptotic expansions.; Reliability (Engineering)
Description: 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.
Notes: Includes bibliographical references (p. 135-144) and index.
Rev. version of: Asymptotische Approximationen für Wahrscheinlichkeitsintegrale.