Anomaly Detection in Random Heterogeneous Media Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion /

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 who...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Simon, Martin (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum, 2015.
Έκδοση:1st ed. 2015.
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03548nam a22004695i 4500
001 978-3-658-10993-6
003 DE-He213
005 20151204160829.0
007 cr nn 008mamaa
008 150723s2015 gw | s |||| 0|eng d
020 |a 9783658109936  |9 978-3-658-10993-6 
024 7 |a 10.1007/978-3-658-10993-6  |2 doi 
040 |d GrThAP 
050 4 |a QA370-380 
072 7 |a PBKJ  |2 bicssc 
072 7 |a MAT007000  |2 bisacsh 
082 0 4 |a 515.353  |2 23 
100 1 |a Simon, Martin.  |e author. 
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. 
250 |a 1st ed. 2015. 
264 1 |a Wiesbaden :  |b Springer Fachmedien Wiesbaden :  |b Imprint: Springer Spektrum,  |c 2015. 
300 |a XIV, 150 p. 27 illus.  |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 
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 Mathematics. 
650 0 |a Partial differential equations. 
650 0 |a Probabilities. 
650 0 |a Physics. 
650 1 4 |a Mathematics. 
650 2 4 |a Partial Differential Equations. 
650 2 4 |a Probability Theory and Stochastic Processes. 
650 2 4 |a Numerical and Computational Physics. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783658109929 
856 4 0 |u http://dx.doi.org/10.1007/978-3-658-10993-6  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)