LEADER 04170nam 22006015 450 001 9910299765203321 005 20220516172806.0 010 $a3-658-10993-9 024 7 $a10.1007/978-3-658-10993-6 035 $a(CKB)3710000000452157 035 $a(EBL)3567846 035 $a(SSID)ssj0001534599 035 $a(PQKBManifestationID)11823034 035 $a(PQKBTitleCode)TC0001534599 035 $a(PQKBWorkID)11494695 035 $a(PQKB)10415840 035 $a(DE-He213)978-3-658-10993-6 035 $a(MiAaPQ)EBC3567846 035 $a(PPN)187686149 035 $a(EXLCZ)993710000000452157 100 $a20150723d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnomaly detection in random heterogeneous media$b[electronic resource] $eFeynman-Kac formulae, stochastic homogenization and statistical inversion /$fby Martin Simon 205 $a1st ed. 2015. 210 1$aWiesbaden :$cSpringer Fachmedien Wiesbaden :$cImprint: Springer Spektrum,$d2015. 215 $a1 online resource (153 p.) 300 $a"Research"--Cover. 311 $a3-658-10992-0 320 $aIncludes bibliographical references. 327 $aPart 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 ?eld models.- Appendix C FEM discretization of the forward problem. 330 $aThis 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. 606 $aPartial differential equations 606 $aProbabilities 606 $aPhysics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 615 0$aPartial differential equations. 615 0$aProbabilities. 615 0$aPhysics. 615 14$aPartial Differential Equations. 615 24$aProbability Theory and Stochastic Processes. 615 24$aNumerical and Computational Physics, Simulation. 676 $a510 700 $aSimon$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755697 906 $aBOOK 912 $a9910299765203321 996 $aAnomaly detection in random heterogeneous media$91522851 997 $aUNINA