國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Anomaly detection in random heteroge...

Simon, Martin.

Anomaly detection in random heterogeneous mediaFeynman-Kac formulae, stochastic homogenization and statistical inversion /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Anomaly detection in random heterogeneous mediaby Martin Simon.
其他題名:	Feynman-Kac formulae, stochastic homogenization and statistical inversion /
作者:	Simon, Martin.
出版者:	Wiesbaden :Springer Fachmedien Wiesbaden :2015.
面頁冊數:	xiv, 151 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Inverse problems (Differential equations)
電子資源:	http://dx.doi.org/10.1007/978-3-658-10993-6
ISBN:	9783658109936 (electronic bk.)

Anomaly detection in random heterogeneous mediaFeynman-Kac formulae, stochastic homogenization and statistical inversion /
Simon, Martin.

Anomaly detection in random heterogeneous mediaFeynman-Kac formulae, stochastic homogenization and statistical inversion /[electronic resource] :by Martin Simon. - Wiesbaden :Springer Fachmedien Wiesbaden :2015. - xiv, 151 p. :ill., digital ;24 cm.

Part I: Probabilistic interpretation of EIT -- Mathematical setting -- Feynman-Kac formulae -- Part II: Anomaly detection in heterogeneous media -- Stochastic homogenization: Theory and numerics -- Statistical inversion -- Appendix A Basic Dirichlet form theory -- Appendix B Random ﬁeld models -- Appendix C FEM discretization of the forward problem.

This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT) Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field whose realizations are rapidly oscillating. For this purpose, he derives Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of the underlying stochastic boundary value problem. The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. Moreover, the author proposes an efficient numerical method in the framework of Bayesian inversion for the practical solution of the stochastic inverse anomaly detection problem. Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems Target Groups Students and researchers in the fields of inverse problems, partial differential equations, probability theory and stochastic processes Practitioners in the fields of tomographic imaging and noninvasive testing via EIT About the Author Martin Simon has worked as a researcher at the Institute of Mathematics at the University of Mainz from 2008 to 2014. During this period he had several research stays at the University of Helsinki. He has recently joined an asset management company as a financial mathematician.

ISBN: 9783658109936 (electronic bk.)

Standard No.: 10.1007/978-3-658-10993-6doiSubjects--Topical Terms:

189581
Inverse problems (Differential equations)

LC Class. No.: QA371

Dewey Class. No.: 515.357

Anomaly detection in random heterogeneous mediaFeynman-Kac formulae, stochastic homogenization and statistical inversion /
LDR:02900nmm a2200313 a 4500 001 472805
003 DE-He213
005 20160223152401.0
006 m d
007 cr nn 008maaau
008 160316s2015 gw s 0 eng d
020 $a 9783658109936 (electronic bk.)
020 $a 9783658109929 (paper)
024 7 $a 10.1007/978-3-658-10993-6 $2 doi
035 $a 978-3-658-10993-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA371
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.357 $2 23
090 $a QA371 $b .S595 2015
100 1 $a Simon, Martin. $3 728099
245 1 0 $a Anomaly detection in random heterogeneous media $h [electronic resource] : $b Feynman-Kac formulae, stochastic homogenization and statistical inversion / $c by Martin Simon.
260 $a Wiesbaden : $b Springer Fachmedien Wiesbaden : $b Imprint: Springer Spektrum, $c 2015.
300 $a xiv, 151 p. : $b ill., digital ; $c 24 cm.
505 0 $a Part I: Probabilistic interpretation of EIT -- Mathematical setting -- Feynman-Kac formulae -- Part II: Anomaly detection in heterogeneous media -- Stochastic homogenization: Theory and numerics -- Statistical inversion -- Appendix A Basic Dirichlet form theory -- Appendix B Random ﬁeld models -- Appendix C FEM discretization of the forward problem.
520 $a This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT) Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field whose realizations are rapidly oscillating. For this purpose, he derives Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of the underlying stochastic boundary value problem. The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. Moreover, the author proposes an efficient numerical method in the framework of Bayesian inversion for the practical solution of the stochastic inverse anomaly detection problem. Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems Target Groups Students and researchers in the fields of inverse problems, partial differential equations, probability theory and stochastic processes Practitioners in the fields of tomographic imaging and noninvasive testing via EIT About the Author Martin Simon has worked as a researcher at the Institute of Mathematics at the University of Mainz from 2008 to 2014. During this period he had several research stays at the University of Helsinki. He has recently joined an asset management company as a financial mathematician.
650 0 $a Inverse problems (Differential equations) $3 189581
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Numerical and Computational Physics. $3 384722
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-658-10993-6
950 $a Mathematics and Statistics (Springer-11649)