Anomaly detection in random heterogeneous media : Feynman-Kac formulae, stochastic homogenization and statistical inversion

Author(s)

Bibliographic Information

Anomaly detection in random heterogeneous media : Feynman-Kac formulae, stochastic homogenization and statistical inversion

Martin Simon ; with a foreword by Lassi Päivärinta

(Research)

Springer Spektrum, c2015

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Note

"Dissertation, Johannes Gutenberg University of Mainz, Germany, 2014"--T.p. verso

Bibliography: p. [137]-150

Description and Table of Contents

Description

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.

Table of Contents

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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Details

  • NCID
    BB19616434
  • ISBN
    • 9783658109929
  • LCCN
    2015945820
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Wiesbaden
  • Pages/Volumes
    xiv, 150 p.
  • Size
    21 cm
  • Classification
  • Parent Bibliography ID
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