Anomaly detection in random heterogeneous media : Feynman-Kac formulae, stochastic homogenization and statistical inversion
著者
書誌事項
Anomaly detection in random heterogeneous media : Feynman-Kac formulae, stochastic homogenization and statistical inversion
（Research）
Springer Spektrum, c2015
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注記
"Dissertation, Johannes Gutenberg University of Mainz, Germany, 2014"--T.p. verso
Bibliography: p. [137]-150
内容説明・目次
内容説明
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.
目次
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.
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