The Resource Anomaly Detection in Random Heterogeneous Media : Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion, by Martin Simon, (electronic resource)

Anomaly Detection in Random Heterogeneous Media : Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion, by Martin Simon, (electronic resource)

Label
Anomaly Detection in Random Heterogeneous Media : Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion
Title
Anomaly Detection in Random Heterogeneous Media
Title remainder
Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion
Statement of responsibility
by Martin Simon
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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. Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems Target Groups Students and researchers in the fields of inverse problems, partial differential equations, probability theory and stochastic processes Practitioners in the fields of tomographic imaging and noninvasive testing via EIT About the Author 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
http://library.link/vocab/creatorName
Simon, Martin
Dewey number
510
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
1lzs61Coze8
Language note
English
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Distribution (Probability theory
  • Partial Differential Equations
  • Probability Theory and Stochastic Processes
  • Numerical and Computational Physics, Simulation
Label
Anomaly Detection in Random Heterogeneous Media : Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion, by Martin Simon, (electronic resource)
Instantiates
Publication
Note
"Research"--Cover
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2015.
Extent
1 online resource (153 p.)
Form of item
online
Isbn
9783658109936
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-658-10993-6
Specific material designation
remote
System control number
  • (CKB)3710000000452157
  • (EBL)3567846
  • (SSID)ssj0001534599
  • (PQKBManifestationID)11823034
  • (PQKBTitleCode)TC0001534599
  • (PQKBWorkID)11494695
  • (PQKB)10415840
  • (DE-He213)978-3-658-10993-6
  • (MiAaPQ)EBC3567846
  • (EXLCZ)993710000000452157
Label
Anomaly Detection in Random Heterogeneous Media : Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion, by Martin Simon, (electronic resource)
Publication
Note
"Research"--Cover
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2015.
Extent
1 online resource (153 p.)
Form of item
online
Isbn
9783658109936
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-658-10993-6
Specific material designation
remote
System control number
  • (CKB)3710000000452157
  • (EBL)3567846
  • (SSID)ssj0001534599
  • (PQKBManifestationID)11823034
  • (PQKBTitleCode)TC0001534599
  • (PQKBWorkID)11494695
  • (PQKB)10415840
  • (DE-He213)978-3-658-10993-6
  • (MiAaPQ)EBC3567846
  • (EXLCZ)993710000000452157

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