Approximation Methods in Probability Theory
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle func
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Vydas Čekanavičius
Approximation Methods in Probability Theory
Universitext
Universitext Series Editors Sheldon Axler San Francisco State University Vincenzo Capasso Università degli Studi di Milano Carles Casacuberta Universitat de Barcelona Angus MacIntyre Queen Mary, University of London Kenneth Ribet University of California, Berkeley Claude Sabbah CNRS, Ecole polytechnique, France Endre Süli University of Oxford Wojbor A. Woyczy´nski Case Western Reserve University, Cleveland, OH
Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well classtested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext. More information about this series at http://www.springer.com/series/223
ˇ Vydas Cekanaviˇ cius
Approximation Methods in Probability Theory
123
ˇ Vydas Cekanaviˇ cius Vilnius University Vilnius, Lithuania
ISSN 0172-5939 Universitext ISBN 978-3-319-34071-5 DOI 10.1007/978-3-319-34072-2
ISSN 2191-6675 (electronic) ISBN 978-3-319-34072-2 (eBook)
Library of Congress Control Number: 2016941172 Mathematics Subject Classification (2010): 62E20, 60E10, 60G50, 60F99, 41A25, 41A27 © Springer International Publishing Switzerland 2016 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface
The limit theorems of probability theory are at the core of multiple models used in the broad field of scientific research. Their main function is
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