Probability, Random Processes, and Ergodic Properties
Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing. It will also interest those working with random or stochastic processes, including mathematic
- PDF / 3,388,657 Bytes
- 348 Pages / 462.948 x 684.444 pts Page_size
- 22 Downloads / 200 Views
Probability, Random Processes, and Ergodic Properties Second Edition
Probability, Random Processes, and Ergodic Properties
Robert M. Gray
Probability, Random Processes, and Ergodic Properties Second Edition
Robert M. Gray Department of Electrical Engineering Stanford University Stanford, CA 94305-4075 USA [email protected]
ISBN 978-1-4419-1089-9 e-ISBN 978-1-4419-1090-5 DOI 10.1007/978-1-4419-1090-5 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009932896 © Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my brother, Peter R. Gray April 1940 – May 2009
Preface
This book has a long history. It began over two decades ago as the first half of a book then in progress on information and ergodic theory. The intent was and remains to provide a reasonably self-contained advanced (at least for engineers) treatment of measure theory, probability theory, and random processes, with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inclined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability or ergodic theory. Much of the material is familiar stuff for mathematicians, but many of the topics and results had not then previously appeared in books. Several topics still find little mention in the more applied literature, including descriptions of random processes as dynamical systems or flows; general alphabet models including standard spaces, Polish spaces, and Lebesgue spaces; nonstationary and nonergodic processes which have stationary and ergodic properties; metrics on random processes which quantify how different they are in ways useful for coding and signal processing; and stationary or sliding-block mappings – coding or filtering – of random processes. The original project grew too large and the first part contained much that would likely bore mathematicians and discourage them from the second part. Hence I followed a suggestion to separate the material and split the project in two. The original justification for the present manuscript was the pragmatic one that it would be a shame to
Data Loading...
