02960nam 2200649 450 99646637290331620220911145504.03-540-49033-710.1007/BFb0073538(CKB)1000000000437191(SSID)ssj0000321452(PQKBManifestationID)12064903(PQKBTitleCode)TC0000321452(PQKBWorkID)10279847(PQKB)11352116(DE-He213)978-3-540-49033-3(MiAaPQ)EBC5585031(Au-PeEL)EBL5585031(OCoLC)1066197259(MiAaPQ)EBC6842206(Au-PeEL)EBL6842206(OCoLC)1136255442(PPN)155195751(EXLCZ)99100000000043719120220911d1994 uy 0engurnn|008mamaatxtccrAsymptotic approximations for probability integrals /Karl Wilhelm Breitung1st ed. 1994.Berlin, Germany :Springer Nature Switzerland AG,[1994]©19941 online resource (X, 154 p.) Lecture Notes in Mathematics ;1592Bibliographic Level Mode of Issuance: Monograph0-387-58617-2 3-540-58617-2 Mathematical preliminaries -- Asymptotic analysis -- Univariate integrals -- Multivariate laplace type integrals -- Approximations for normal integrals -- Arbitrary probability integrals -- Crossing rates of stochastic processes.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.Lecture notes in mathematics (Springer-Verlag) ;1592.Stochastic processesReliability (Engineering)Asymptotic expansionsStochastic processes.Reliability (Engineering)Asymptotic expansions.519.2Breitung Karl Wilhelm1953-60691MiAaPQMiAaPQMiAaPQBOOK996466372903316Asymptotic approximations for probability integrals78143UNISA