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Titlebook: Anomaly Detection in Random Heterogeneous Media; Feynman-Kac Formulae Martin Simon Book 2015 Springer Fachmedien Wiesbaden 2015 Calderón’s

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发表于 2025-3-21 17:39:51 | 显示全部楼层 |阅读模式
期刊全称Anomaly Detection in Random Heterogeneous Media
期刊简称Feynman-Kac Formulae
影响因子2023Martin Simon
视频videohttp://file.papertrans.cn/159/158034/158034.mp4
发行地址Publication in the field of natural and mathematical sciences.Includes supplementary material:
图书封面Titlebook: Anomaly Detection in Random Heterogeneous Media; Feynman-Kac Formulae Martin Simon Book 2015 Springer Fachmedien Wiesbaden 2015 Calderón’s
影响因子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. 
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https://doi.org/10.1007/978-3-642-58393-3ed on the first stage results is defined and the resulting posterior distribution is sampled via Markov chain Monte Carlo. We provide the theoretical foundation of the proposed method, discuss different aspects of a numerical implementation and present numerical experiments to support our findings.
发表于 2025-3-22 05:17:39 | 显示全部楼层
Stochastic homogenization: Theory and numericsato, Kim and Cule [159]. From a mathematical point of view, the novelty of the proposed method lies in the fact that it is based on the aforementioned stochastic homogenization result, that is, on simulation of the underlying diffusion process rather than on the usual discretization of the so-called ..
发表于 2025-3-22 12:18:50 | 显示全部楼层
Statistical inversioned on the first stage results is defined and the resulting posterior distribution is sampled via Markov chain Monte Carlo. We provide the theoretical foundation of the proposed method, discuss different aspects of a numerical implementation and present numerical experiments to support our findings.
发表于 2025-3-22 12:53:26 | 显示全部楼层
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
发表于 2025-3-22 19:14:02 | 显示全部楼层
Barbara Ruttmann,Karl Solchenbachontrast to this well-studied situation, the underlying reflecting diffusion processes in this work are constructed via Dirichlet form theory, which has emerged as a powerful tool when it comes to studying boundary value problems with non-smooth coefficients, boundaries and data.
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发表于 2025-3-23 03:44:56 | 显示全部楼层
Book 2015phy (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
发表于 2025-3-23 08:54:38 | 显示全部楼层
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