An Introduction to Probability and Stochastic Processes
These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabil
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(continued after index)
Marc A. Berger
An Introduction to Probability and Stochastic Processes With 19 Illustrations
Springer-Verlag New Yark Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest
Marc A. Berger School of Mathematics Georgia Institute of Technology Atlanta, GA 30332-0269 USA
Editorial Board
Stephen Fienberg
Ingram Olkin
York University North York, Ontario N3J IP3 Canada
Department of Statistics Stanford University Stanford, CA 94305 USA
Cover illustration: A zoom-in view of a fractal dragon set. This image is generated from a 2-map iterated function system. (See color plate 11.)
Mathematics Subject Classifications (1991): 60-01, 60E05, 60110, 60127, 60E1O, 60F05, 60F15, 60GI0,47A35 Library of Congress Cataloging-in-Publication Data Berger, Marc A., 1955An introduction to probability and stochastic processes / Marc A. Berger. p. cm. Includes bibliographical references and index. ISBN·13:978-1-4612-7643-2 1. Probabilities. 2. Stochastic processes. I. Title. CA273.B48 1992 519.2-dc20 91-43019 Printed on acid-free paper.
© 1993 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1993 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 New York. Inc., 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. Production managed by Henry Krell, manufacturing supervised by Vincent Scelta. Typeset by Asco Trade Typesetting Ltd., Hong Kong. 987654321 ISBN
