AHA-BUCH

Anomaly Detection in Random Heterogeneous Media

Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion
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ISBN-13:
9783658109929
Einband:
Book
Erscheinungsdatum:
30.07.2015
Seiten:
150
Autor:
Martin Simon
Gewicht:
224 g
Format:
211x146x15 mm
Sprache:
Englisch
Beschreibung:

99
Part 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.
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.