Theory and Simulation of Random Phenomena Mathematical Foundations a

The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such

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Ettore Vitali · Mario Motta  Davide Emilio Galli

Theory and Simulation of Random Phenomena Mathematical Foundations and Physical Applications

UNITEXT for Physics Series editors Paolo Biscari, Milano, Italy Michele Cini, Roma, Italy Attilio Ferrari, Torino, Italy Stefano Forte, Milano, Italy Morten Hjorth-Jensen, Oslo, Norway Nicola Manini, Milano, Italy Guido Montagna, Pavia, Italy Oreste Nicrosini, Pavia, Italy Luca Peliti, Napoli, Italy Alberto Rotondi, Pavia, Italy

UNITEXT for Physics series, formerly UNITEXT Collana di Fisica e Astronomia, publishes textbooks and monographs in Physics and Astronomy, mainly in English language, characterized of a didactic style and comprehensiveness. The books published in UNITEXT for Physics series are addressed to graduate and advanced graduate students, but also to scientists and researchers as important resources for their education, knowledge and teaching.

More information about this series at http://www.springer.com/series/13351

Ettore Vitali Mario Motta Davide Emilio Galli •

Theory and Simulation of Random Phenomena Mathematical Foundations and Physical Applications

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Ettore Vitali Department of Physics College of William and Mary Williamsburg USA

Davide Emilio Galli Department of Physics University of Milan Milan Italy

Mario Motta Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena USA

ISSN 2198-7882 ISSN 2198-7890 (electronic) UNITEXT for Physics ISBN 978-3-319-90514-3 ISBN 978-3-319-90515-0 (eBook) https://doi.org/10.1007/978-3-319-90515-0 Library of Congress Control Number: 2018939455 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms 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 specific 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered c