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000728347 1001_ $$aSimon, Martin,$$eauthor.
000728347 24510 $$aAnomaly detection in random heterogeneous media$$h[electronic resource] :$$bFeynman-Kac formulae, stochastic homogenization and statistical inversion /$$cMartin Simon ; with a foreword by Prof. Dr. Lassi Päivärinta.
000728347 264_1 $$aWiesbaden :$$bSpringer Spektrum,$$c2015.
000728347 300__ $$a1 online resource (xiv, 150 pages) :$$billustrations
000728347 336__ $$atext$$btxt$$2rdacontent
000728347 337__ $$acomputer$$bc$$2rdamedia
000728347 338__ $$aonline resource$$bcr$$2rdacarrier
000728347 500__ $$a"Dissertation, Johannes Gutenberg University of Mainz, Germany, 2014."
000728347 504__ $$aIncludes bibliographical references.
000728347 506__ $$aAccess limited to authorized users.
000728347 520__ $$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.
000728347 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 29, 2015).
000728347 650_0 $$aInverse problems (Differential equations)
000728347 852__ $$bebk
000728347 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-658-10993-6$$zOnline Access$$91397441.1
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