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Anomaly Detection in Random Heterogeneous Media: Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion
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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.
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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.
Biografía del autor:
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.
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- VerlagSpringer Spektrum
- Erscheinungsdatum2015
- ISBN 10 3658109920
- ISBN 13 9783658109929
- EinbandRústica
- Auflage1
- Anzahl der Seiten164
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Anomaly Detection in Random Heterogeneous Media : Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion
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Springer Fachmedien Wiesbaden
(2015)
ISBN 10: 3658109920
ISBN 13: 9783658109929
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Buchbeschreibung Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9783658109929
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