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Probability, Random Processes, and Ergodic Properties
This book is a self-contained treatment of the theory of probability, random processes. It is intended to lay solid theoretical foundations for advanced probability, that is, for measure and integration theory, and to develop in depth the long term time average behavior of measurements made on random processes with general output alphabets. Unlike virtually all texts on the topic, considerable space is devoted to processes that violate the usual assumptions of stationarity and ergodicity, yet which still possess the fundamental properties of convergence of long term averages to appropriate expectations. The theory of asymtotically mean stationary processes and the ergodic decomposition are both treated in depth for both one-sided and two-sided random processes. In addition, the book treats many of the fundamental results such as the Kolmogorov extension theorem and the ergodic decomposition theorem. Much of the material has not previously appeared in book form, and the treatment takes advantage of many recent generalizations and simplifications.
Hardcover
First published December 18, 1987
15 people want to read
About the author
Robert M. Gray
19 books5 followersRobert M. Gray, of Stanford University.
See also:
Robert M. Gray Jr., editor of Technology Integration in Higher Education.
Robert M. Gray, author of The Church and the Older Person.
Robert M. Gray was born in San Diego, Calif., on November 1, 1943. He received the B.S. and M.S. degrees from M.I.T. in 1966 and the Ph.D. degree from U.S.C. in 1969, all in Electrical Engineering. Since 1969 he has been with Stanford University, where he is currently the Lucent Technologies Professor of Engineering, Emeritus, and Professor of Electrical Engineering, Emeritus. His research interests are in information theory and signal processing, especially in the theory and practice of quantization, compression, and classification.
He was a member of the Board of Governors of the IEEE Information Theory Group (1974-1980, 1985-1988) and of the IEEE Signal Processing Society (1998-2001). He was Associate Editor for Source Coding (1977-1980) and Editor-in-Chief (1980-1983) of the IEEE Transactions on Information Theory. He is currently the Editor-in-Chief of Foundations and Trends in Signal Processing. He was Co-Chair of the 1993 IEEE International Symposium on Information Theory and Program Co-Chair of the 1997 and 2004 IEEE International Conference on Image Processing.
He is a Fellow of the Institute of Mathematical Statistics and the IEEE and has held fellowships from the Japan Society for the Promotion of Science at the University of Osaka (1981), the John Simon Guggenheim Foundation at the University of Paris XI (1982), and NATO/Consiglio Nazionale delle Ricerche at the University of Naples (1990). During spring 1995 he was a Vinton Hayes Visiting Scholar at the Division of Applied Sciences of Harvard University. He is a Faculty Affiliate of the Clayman Institute for Gender Studies at Stanford University, where he was a Faculty Research Fellow during the 2008-2009 academic year.
He was corecipient of the 1976 IEEE Information Theory Group Paper Award and the 1983 IEEE ASSP Senior Award. He was awarded an IEEE Centennial medal (1984) and an IEEE Third Millennium Medal (2000). He received the 1993 Society Award, the 1998 Technical Achievement Award, the 2005 Meritorious Service Award, and the 2009 Education Award from the IEEE Signal Processing Society. He received a Golden Jubilee Award for Technological Innovation (1998) and the 2008 Shannon Award from the IEEE Information Theory Society. He received the 2008 IEEE Jack S. Kilby Signal Processing Medal. He received a 2002 Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM) and the 2003 Distinguished Alumni in Academia Award from the University of Southern California. He is a member of the National Academy of Engineering (2007). He holds an Advanced Class Amateur Radio License (KB6XQ).
See also:
Robert M. Gray Jr., editor of Technology Integration in Higher Education.
Robert M. Gray, author of The Church and the Older Person.
Robert M. Gray was born in San Diego, Calif., on November 1, 1943. He received the B.S. and M.S. degrees from M.I.T. in 1966 and the Ph.D. degree from U.S.C. in 1969, all in Electrical Engineering. Since 1969 he has been with Stanford University, where he is currently the Lucent Technologies Professor of Engineering, Emeritus, and Professor of Electrical Engineering, Emeritus. His research interests are in information theory and signal processing, especially in the theory and practice of quantization, compression, and classification.
He was a member of the Board of Governors of the IEEE Information Theory Group (1974-1980, 1985-1988) and of the IEEE Signal Processing Society (1998-2001). He was Associate Editor for Source Coding (1977-1980) and Editor-in-Chief (1980-1983) of the IEEE Transactions on Information Theory. He is currently the Editor-in-Chief of Foundations and Trends in Signal Processing. He was Co-Chair of the 1993 IEEE International Symposium on Information Theory and Program Co-Chair of the 1997 and 2004 IEEE International Conference on Image Processing.
He is a Fellow of the Institute of Mathematical Statistics and the IEEE and has held fellowships from the Japan Society for the Promotion of Science at the University of Osaka (1981), the John Simon Guggenheim Foundation at the University of Paris XI (1982), and NATO/Consiglio Nazionale delle Ricerche at the University of Naples (1990). During spring 1995 he was a Vinton Hayes Visiting Scholar at the Division of Applied Sciences of Harvard University. He is a Faculty Affiliate of the Clayman Institute for Gender Studies at Stanford University, where he was a Faculty Research Fellow during the 2008-2009 academic year.
He was corecipient of the 1976 IEEE Information Theory Group Paper Award and the 1983 IEEE ASSP Senior Award. He was awarded an IEEE Centennial medal (1984) and an IEEE Third Millennium Medal (2000). He received the 1993 Society Award, the 1998 Technical Achievement Award, the 2005 Meritorious Service Award, and the 2009 Education Award from the IEEE Signal Processing Society. He received a Golden Jubilee Award for Technological Innovation (1998) and the 2008 Shannon Award from the IEEE Information Theory Society. He received the 2008 IEEE Jack S. Kilby Signal Processing Medal. He received a 2002 Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM) and the 2003 Distinguished Alumni in Academia Award from the University of Southern California. He is a member of the National Academy of Engineering (2007). He holds an Advanced Class Amateur Radio License (KB6XQ).
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Displaying 1 of 1 review
January 5, 2018
This book teaches probability theory in a nonstandard way, compared to most modern first-year graduate courses in probability theory. I learned a lot from this book.
However, the book doesn't seem to be ready for publication; some of the exercises are wrong (such as ____ and ____ (TO UPDATE LATER)), there were very few exercises outside of Chapters 1, 7 and 8 (for example, none at all in Chapters 9 (Process Approximation and Metrics) and 10 (The Ergodic Decomposition)) and there were many, many typos (on the order of a couple per page). I'm concerned about the exercise selection because in my opinion, exercises are extremely important in learning math.
However, the book doesn't seem to be ready for publication; some of the exercises are wrong (such as ____ and ____ (TO UPDATE LATER)), there were very few exercises outside of Chapters 1, 7 and 8 (for example, none at all in Chapters 9 (Process Approximation and Metrics) and 10 (The Ergodic Decomposition)) and there were many, many typos (on the order of a couple per page). I'm concerned about the exercise selection because in my opinion, exercises are extremely important in learning math.
Displaying 1 of 1 review