Dependence in Probability and Statistics A Survey of Recent Results
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Peter Huber Murray Rosenblatt series editors
Ernst Eberlein Murad S. Taqqu editors
Dependence in Probability and Statistics A Survey of Recent Results (Oberwolfach, 1985)
1986
Springer Science+ Business Media, LLC
Ernst Eberlein Institut fur Mathematische Stochastik Uni versităt Freiburg 7800 Freiburg i. Br. Federal Republic of Germany
Murad S. Taqqu Department of Mathematics Boston University Boston, MA 02215 U.S.A.
Library of Congress Cataloging in Publicat ion Data Dependence in probability and statistics. (Progress in probability and statistics; voi. 11) lncludes bibliographies. 1. Random 1. Random variables. 2. Probabilities. 3. Mathematical statistics. 1. Eberlein. Ernst. Il. Taqqu, Murad S. III. Series: Progress in probability and statistics; v. Il. QA273. 18.047 1986 519.2 86- 12927 CIP-Kurztitelaufnahme der Deutschen Bibliothek Dependence in probability and statistics.Boston ; Basel ; Stuttgart : Birkhăuser. 1986. (Progress in probability and statistics ; Voi. Il) ISBN 978·1-4615·8163·5
NE:GT Ali rights reserved. No part of th is publication may be reproduced. stored in a retrieval system. or transmitted. in any form or by any means, electronic. mechanical. photocopying. recording. or otherwise. without prior permission of the copyright owner. © Springer Science+Business Media New York 1986 OriginaUy publisbed by Birkhăuser Boston, lnc., in 1986 ISBN 978-1-4615-8163-5 ISBN 978-1-4615 -8162-8 (eBook) DOI 10.1007/978-1-4615-8162-8
PREFACE
Practitioners and researchers in probability and statistics often work with dependent random variables. It is therefore important to understand dependence structures and in particular the limiting results that can be obtained under various dependence assumptions. It is now weil known that a great number of limit theorems which in the classical
approach were always studied under the assumption that the underlying random variables were independent, continue to hold under certain dependence structures. Independence is not necessary. On the other hand, as dependence becomes stronger, at a certain point new phenomena arise. One is then led to ask: how much dependence, qualitatively and quantitatively, is allowed for the classical limit results to hold; and what are the results when dependence becomes stronger. Our understanding of the complex relationships between dependence assumptions and limiting procedures has improved considerably during the last years. It is the purpose of this book to cover in an expository fashion a broad spectrum of recent results. Some of the theorems appear here for the first time. Because of the great variety of dependence structures, it would be difficult for a single author to treat so wide a topic. The contributors to this book participated in a conference on this subject held at the Mathematical Research Institute Oberwolfach in April 1985.
The book is aimed at an audience that is well-versed in probability and statistics but not necessarily weil acquainted with the subject matter of the various papers. These papers tie together kn
