Probability Theory Independence, Interchangeability, Martingales
Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for marti
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Probability Theory Independence, In terchangea bili ty, Martingales Second Edition
Springer-Verlag New York Berlin Heidelberg London Paris Tokyo
Yuan Shih Chow Department of Mathematical Statistics Columbia University New York, NY 10027
Henry Teicher Department of Statistics Rutgers University New Brunswick, NJ 08903
Editorial Board
Ingram Olkin Department of Statistics Stanford University Stanford, CA 94305
Stephen Fienberg Department of Statistics Carnegie-Mellon University Pittsburgh, PA 15213
Mathematics Subject Classification (1980): 60-01, 60E05, 60Fxx
Library of Congress Cataloging in Publication Data Chow, Yuan Shih, 1924Probability theory: independence, interchangeability, martingales /Yuan Shih Chow, Henry Teicher.-2nd ed. cm.-(Springer texts in statistics) p. Includes bibliographies and index. 1. Probabilities. 2. Martingales (Mathematics) I. Teicher, Henry. II. Title. III. Series. QA273.C573 1988 519.2-dcI9 87-34661
© 1978, 1988 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 2nd edition 1988 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc. in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Typeset by Asco Trade Typesetting Ltd., Hong Kong. 9 8 7 6 543 2 1 ISBN-13: 978-1-4684-0506-4 DOl: 10.1007/978-1-4684-0504-0
e-ISBN-13: 978-1-4684-0504-0
To our teachers J. L. Dooh and J. WolJowitz
Preface to the Second Edition
Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the
