Probability, Random Processes, and Ergodic Properties
By: by Robert M. Gray
Publisher: Springer New York
Published: 1988
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 295
ISBN-13: 9781475720266; 9781475720242
Subjects: Engineering; Engineering mathematics; Telecommunication
Description: 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.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.
Table of contents: title: Contents: Probability and Random Processes; title: Standard Alphabets; title: Borel Spaces and Polish Alphabets; title: Averages; title: Conditional Probability and Expectation; title: Ergodic Properties; title: Ergodic Theorems; title: Spaces of Measures and the Ergodic Decomposition; title: Bibliography; title: Index.