Anomaly Detection in Random Heterogeneous Media (eBook)

Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion

Martin Simon (Autor)

eBook Download: PDF

2015 | 1st ed. 2015
XIV, 150 Seiten
Springer Fachmedien Wiesbaden GmbH (Verlag)
978-3-658-10993-6 (ISBN)

Infos

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. 

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. 

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 23.7.2015
• Zusatzinfo: XIV, 150 p. 27 illus.
• Verlagsort: Wiesbaden
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Schlagworte: applied probability theory • Calderón’s inverse conductivity problem • EIT • Electrical Impedance Tomography • Partial differential equations • Random Media • statistical inverse problems • stochastic analysis
• ISBN-10: 3-658-10993-9 / 3658109939
• ISBN-13: 978-3-658-10993-6 / 9783658109936