Author | Gray, Robert M. author |
---|---|

Title | Probability, Random Processes, and Ergodic Properties [electronic resource] / by Robert M. Gray |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1988 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-2024-2 |

Descript | XVI, 295 p. online resource |

SUMMARY

This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time 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 inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the 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 waste all the effort thus far expended. A more idealistic motivation was that the presentation bad merit as filling a unique, albeit smaIl, hole in the literature

CONTENT

1. Probability and Random Processes -- 2. Standard Alphabets -- 3. Borel Spaces and Polish Alphabets -- 4. Averages -- 5. Conditional Probability and Expectation -- 6. Ergodic Properties -- 7. Ergodic Theorems -- 8. Spaces of Measures and the Ergodic Decomposition

Mathematics
Coding theory
Probabilities
Applied mathematics
Engineering mathematics
Electrical engineering
Mathematics
Probability Theory and Stochastic Processes
Coding and Information Theory
Signal Image and Speech Processing
Appl.Mathematics/Computational Methods of Engineering
Communications Engineering Networks