國立虎尾科技大學 |

Analysis and Approximation of Rare Events = Representations and Weak Convergence Methods /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Analysis and Approximation of Rare Events/ by Amarjit Budhiraja, Paul Dupuis.
Reminder of title:	Representations and Weak Convergence Methods /
Author:	Budhiraja, Amarjit.
other author:	Dupuis, Paul.
Description:	XIX, 574 p. 14 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Probabilities. -
Online resource:	https://doi.org/10.1007/978-1-4939-9579-0
ISBN:	9781493995790

Analysis and Approximation of Rare Events = Representations and Weak Convergence Methods /
Budhiraja, Amarjit.

Analysis and Approximation of Rare EventsRepresentations and Weak Convergence Methods /[electronic resource] :by Amarjit Budhiraja, Paul Dupuis. - 1st ed. 2019. - XIX, 574 p. 14 illus., 1 illus. in color.online resource. - Probability Theory and Stochastic Modelling,942199-3130 ;. - Probability Theory and Stochastic Modelling,76.

Preliminaries and elementary examples -- Discrete time processes -- Continuous time processes -- Monte Carlo approximation.

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.

ISBN: 9781493995790

Standard No.: 10.1007/978-1-4939-9579-0doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Analysis and Approximation of Rare Events = Representations and Weak Convergence Methods /
LDR:02910nam a22004335i 4500 001 1006082
003 DE-He213
005 20201222013238.0
007 cr nn 008mamaa
008 210106s2019 xxu| s |||| 0|eng d
020 $a 9781493995790 $9 978-1-4939-9579-0
024 7 $a 10.1007/978-1-4939-9579-0 $2 doi
035 $a 978-1-4939-9579-0
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Budhiraja, Amarjit. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1299565
245 1 0 $a Analysis and Approximation of Rare Events $h [electronic resource] : $b Representations and Weak Convergence Methods / $c by Amarjit Budhiraja, Paul Dupuis.
250 $a 1st ed. 2019.
264 1 $a New York, NY : $b Springer US : $b Imprint: Springer, $c 2019.
300 $a XIX, 574 p. 14 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 94
505 0 $a Preliminaries and elementary examples -- Discrete time processes -- Continuous time processes -- Monte Carlo approximation.
520 $a This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
650 0 $a Probabilities. $3 527847
650 0 $a Applied mathematics. $3 1069907
650 0 $a Engineering mathematics. $3 562757
650 0 $a Numerical analysis. $3 527939
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Mathematical and Computational Engineering. $3 1139415
650 2 4 $a Numerical Analysis. $3 671433
700 1 $a Dupuis, Paul. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1299566
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9781493995776
776 0 8 $i Printed edition: $z 9781493995783
776 0 8 $i Printed edition: $z 9781493996223
830 0 $a Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 76 $3 1254049
856 4 0 $u https://doi.org/10.1007/978-1-4939-9579-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)