LEADER 02960nam 2200649 450 001 996466372903316 005 20220911145504.0 010 $a3-540-49033-7 024 7 $a10.1007/BFb0073538 035 $a(CKB)1000000000437191 035 $a(SSID)ssj0000321452 035 $a(PQKBManifestationID)12064903 035 $a(PQKBTitleCode)TC0000321452 035 $a(PQKBWorkID)10279847 035 $a(PQKB)11352116 035 $a(DE-He213)978-3-540-49033-3 035 $a(MiAaPQ)EBC5585031 035 $a(Au-PeEL)EBL5585031 035 $a(OCoLC)1066197259 035 $a(MiAaPQ)EBC6842206 035 $a(Au-PeEL)EBL6842206 035 $a(OCoLC)1136255442 035 $a(PPN)155195751 035 $a(EXLCZ)991000000000437191 100 $a20220911d1994 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAsymptotic approximations for probability integrals /$fKarl Wilhelm Breitung 205 $a1st ed. 1994. 210 1$aBerlin, Germany :$cSpringer Nature Switzerland AG,$d[1994] 210 4$dİ1994 215 $a1 online resource (X, 154 p.) 225 1 $aLecture Notes in Mathematics ;$v1592 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-58617-2 311 $a3-540-58617-2 327 $aMathematical preliminaries -- Asymptotic analysis -- Univariate integrals -- Multivariate laplace type integrals -- Approximations for normal integrals -- Arbitrary probability integrals -- Crossing rates of stochastic processes. 330 $aThis book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1592. 606 $aStochastic processes 606 $aReliability (Engineering) 606 $aAsymptotic expansions 615 0$aStochastic processes. 615 0$aReliability (Engineering) 615 0$aAsymptotic expansions. 676 $a519.2 700 $aBreitung$b Karl Wilhelm$f1953-$060691 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466372903316 996 $aAsymptotic approximations for probability integrals$978143 997 $aUNISA