Asymptotic Approximations for Probability Integrals
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 exampl
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1592
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, Zurich F. Takens, Groningen
1592
Karl Wilhelm Breitung
AsymptoticApproximations for Probability Integrals
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Author Karl Wilhelm Breitung Department of Civil Engineering University of Calgary 2500 University Drive, N.W. Calgary, Alberta T2N 1N4, Canada
Mathematics Subject Classification (1991): 41A60, 41A63, 60F10, 60G 15, 60G70, 62N05, 62P99, 90B25
ISBN 3-540-58617-2 Springer-Verlag Berlin Heidelberg New York CIP-Data applied for This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1994 Printed in Germany Typesetting: Camera ready by author SPIN: 10130174 46/3140-543210 - Printed on acid-free paper
Preface In this lecture note asymptotic approximation methods for multivariate integrals, especially probability integrals, are developed. It is a revised version of my habilitationsschrijt "Asymptotische Approximationen fur Wahrscheinlichkeitsintegrale". The main part of this research was done when I worked at the Technical University and the University of Munich. The motivation to study these problems comes from my work in the research project "Zuverliissigkeitstheorie der Bauwerke" (reliability theory of structures) at the Technical University of Munich in the department of civil engineering. For the tolerant support of the mathematical research in this project I would like to thank Prof. Dr.Ing. H. Kupfer. I am grateful to Prof. Dr.Ing. R. Rackwitz and Prof. Dr.Ing. G.!. Schueller that they made me clear the engineering topics of reliability theory and helped me in my research. Further I would like to thank my former colleagues at the Technical University of Munich and at the University of Munich which supported me during my work at these universities: Dr.Ing. B. FieBler, Dr. M. Hohenbichler, Dr. A. Rosch, Dr. H. Schmidbauer and Dr. C. Schneider. Additionally I would like to express my gratitude to Prof. Dr. F. Ferschl for pointing out occasional errors and misprints in the original German version. The major part of this revision was made when I stayed as visiting fellow at the University of New South Wales in 1991. I would like to thank especially Prof. A. M. Hasofer for his help and for his kind invitation to the University of New South Wales and to express my delight at having worked there. For their help and discussions I thank wholeheartedly Prof. Dr. F. Casciati, Pro
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