Asymptotic Approximations for Probability Integrals
Breitung, Karl Wilhelm.
Asymptotic Approximations for Probability Integrals [electronic resource] / by Karl Wilhelm Breitung. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1592 0075-8434 ; . - Lecture Notes in Mathematics, 1592 .
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.
9783540490333
10.1007/BFb0073538 doi
Engineering mathematics.
Distribution (Probability theory.
Global differential geometry.
Mathematical and Computational Engineering.
Probability Theory and Stochastic Processes.
Differential Geometry.
Theoretical, Mathematical and Computational Physics.
TA329-348 TA640-643
519
Asymptotic Approximations for Probability Integrals [electronic resource] / by Karl Wilhelm Breitung. - X, 154 p. online resource. - Lecture Notes in Mathematics, 1592 0075-8434 ; . - Lecture Notes in Mathematics, 1592 .
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.
9783540490333
10.1007/BFb0073538 doi
Engineering mathematics.
Distribution (Probability theory.
Global differential geometry.
Mathematical and Computational Engineering.
Probability Theory and Stochastic Processes.
Differential Geometry.
Theoretical, Mathematical and Computational Physics.
TA329-348 TA640-643
519