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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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Detail Information

Series Title

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Call Number

519.2 SIM a

Publisher

Wiesbaden : Springer Spektrum Wiesbaden., 2015

Collation

XIV, 150

Language

English

ISBN/ISSN

978-3-658-10993-6

Classification

519.2

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

Ed. 1

Subject(s)

Differential equations
Probability Theory

Specific Detail Info

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Statement of Responsibility

Martin Simon

Other Information

Cataloger

umi

Source

https://link.springer.com/content/pdf/10.1007/978-3-658-10993-6.pdf?pdf=button

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