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OverviewThis 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. Full Product DetailsAuthor: Martin SimonPublisher: Springer Fachmedien Wiesbaden Imprint: Springer Spektrum Edition: 1st ed. 2015 Dimensions: Width: 14.80cm , Height: 1.00cm , Length: 21.00cm Weight: 2.205kg ISBN: 9783658109929ISBN 10: 3658109920 Pages: 150 Publication Date: 30 July 2015 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPart 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.ReviewsAuthor InformationMartin 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. Tab Content 6Author Website:Countries AvailableAll regions |
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