Feynman-Kac formulae
In this chapter, we establish the connection between the deterministic EIT forward problem and the class of reflecting diffusion processes. We proceed along the lines of the recent paper [137] by Piiroinen and the author: We derive Feynman-Kac formulae in
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Martin Simon
Anomaly Detection in Random Heterogeneous Media Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion With a Foreword by Prof. Dr. Lassi Päivärinta
Martin Simon Mainz, Germany Dissertation, Johannes Gutenberg University of Mainz, Germany, 2014
ISBN 978-3-658-10992-9 ISBN 978-3-658-10993-6 (eBook) DOI 10.1007/978-3-658-10993-6 Library of Congress Control Number: 2015945820 Springer Spektrum © Springer Fachmedien Wiesbaden 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speci¿cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro¿lms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a speci¿c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Spektrum is a brand of Springer Fachmedien Wiesbaden Springer Fachmedien Wiesbaden is part of Springer Science+Business Media (www.springer.com)
To my parents Andrea and Alfred, my wife Lilian and my daughter Luisa.
Foreword Inverse problems constitute an interdisciplinary field of science concentrating on the mathematical theory and practical interpretation of indirect measurements. Possible applications include medical imaging, atmospheric remote sensing, industrial process monitoring and astronomical imaging. Innovations such as computerized tomography, magnetic resonance imaging and exploration of the interior of the earth by using earthquake data are typical examples where mathematical research has played a major role. The common feature of all these problems is their extreme sensitivity to measurement noise. Dealing with this so-called ill-posedness both theoretically and practically often requires genuine scientific progress, say in geometry, stochastics or analysis. Through mathematical modeling it becomes in turn possible to bring these theoretical inventions to real life applications. Martin Simon’s book is a multi-field work, mainly in the fields of applied probability theory and statistical inverse problems. The work is motivated by an important inverse problem, namely electrical impedance tomography (EIT) which is also called Calderón’s inverse conductivity problem. The author is interested in practical real-life applicatio
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