Anomaly detection in random heterogeneous media [electronic resource] : Feynman-Kac formulae, stochastic homogenization and statistical inversion / Martin Simon ; with a foreword by Prof. Dr. Lassi Päivärinta.
2015
QA371
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Title
Anomaly detection in random heterogeneous media [electronic resource] : Feynman-Kac formulae, stochastic homogenization and statistical inversion / Martin Simon ; with a foreword by Prof. Dr. Lassi Päivärinta.
Author
Simon, Martin, author.
ISBN
9783658109936 electronic book
3658109939 electronic book
9783658109929
3658109939 electronic book
9783658109929
Published
Wiesbaden : Springer Spektrum, 2015.
Language
English
Description
1 online resource (xiv, 150 pages) : illustrations
Call Number
QA371
Dewey Decimal Classification
515/.357
Summary
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.
Note
"Dissertation, Johannes Gutenberg University of Mainz, Germany, 2014."
Bibliography, etc. Note
Includes bibliographical references.
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Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 29, 2015).
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