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Probability, random processes, and ergodic properties

Author: SpringerLink (Service en ligne)
Publisher: Springer US, 2009.
Series: SpringerLink Engineering.
Edition/Format:   Computer file : English

In this new edition of this classic text, much of the material has been rearranged and revised for pedagogical reasons. Many classic inequalities and proofs are now incorporated into the text, and  Read more...


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Material Type: Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: SpringerLink (Service en ligne)
ISBN: 9781441910905 1441910905 9781441910899 1441910891
OCLC Number: 475539411
Notes: Titre de l'écran-titre (visionné le 6 nov. 2009).
In SpringerLink Engineering.
Contents: Introduction.- Probability Spaces.- Sample Spaces.- Metric Spaces.- Measurable Spaces.- Borel Measurable Spaces.- Polish Spaces.- Probability Spaces.- Complete Probability Spaces.- Extension.- Random Processes and Dynamical Systems.- Measurable Functions and Random Variables.- Approximation of Random Variables and Distributions.- Random Processes and Dynamical Systems.- Distributions.- Equivalent Random Processes.- Codes, Filters, and Factors.- Isomorphism.- Standard Alphabets.- Extension of Probability Measures.- Standard Spaces.- Some Properties of Standard Spaces.- Simple Standard Spaces.- Characterization of Standard Spaces.- Extension in Standard Spaces.- The Kolmogorov Extension Theorem.- Bernoulli Processes.- Discrete B-Processes.- Extension Without a Basis.- Lebesgue Spaces.- Lebesgue Measure on the Real Line.- Standard Borel Spaces.- Products of Polish Spaces.- Subspaces of Polish Spaces.- Polish Schemes.- Product Measures.- IID Random Processes and B-processes.- Standard Spaces vs. Lebesgue Spaces.- Averages.- Discrete Measurements.- Quantization.- Expectation.- Limits.- Inequalities.- Integrating to the Limit.- Time Averages.- Convergence of Random Variables.- Stationary Random Processes.- Block and Asymptotic Stationarity.- Conditional Probability and Expectation.- Measurements and Events.- Restrictions of Measures.- Elementary Conditional Probability.- Projections.- The Radon-Nikodym Theorem.- Probability Densities.- Conditional Probability.- Regular Conditional Probability.- Conditional Expectation.- Independence and Markov Chains.- Ergodic Properties.- Ergodic Properties of Dynamical Systems.- Implications of Ergodic Properties.- Asymptotically Mean Stationary Processes.- Recurrence.- Asymptotic Mean Expectations.- Limiting Sample Averages.- Ergodicity.- Block Ergodic and Totally Ergodic Processes.- The Ergodic Decomposition.- Ergodic Theorems.- The Pointwise Ergodic Theorem.- Mixing Random Processes.- Block AMS Processes.- The Ergodic Decomposition of AMS Systems.- The Subadditive Ergodic Theorem.- Process Approximation and Metrics.- Distributional Distance.- Optimal Coupling Distortion and dp Distance.- Prohorov and Variational Distances.- Evaluating dp .- Measures on Measures.- The Ergodic Decomposition.- The Ergodic Decomposition Revisited.- The Ergodic Decomposition of Markov Processes.- Barycenters.- Affine Functions of Measures.- The Ergodic Decomposition of Affine Functionals.- References.-
Series Title: SpringerLink Engineering.


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From the reviews of the second edition:"This is the second edition of the classic text book by Robert M. Gray on information theory for engineers working in information theory and signal processing. Read more...

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