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The Resource Probability, random processes, and ergodic properties, Robert M. Gray

Probability, random processes, and ergodic properties, Robert M. Gray

Label
Probability, random processes, and ergodic properties
Title
Probability, random processes, and ergodic properties
Statement of responsibility
Robert M. Gray
Creator
Subject
Language
eng
Summary
"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 mathematicians, statisticians, and economists."--Publisher's website
Cataloging source
BTCTA
http://library.link/vocab/creatorDate
1943-
http://library.link/vocab/creatorName
Gray, Robert M.
Illustrations
illustrations
Index
index present
LC call number
QA273
LC item number
.G683 2009
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Probabilities
  • Measure theory
  • Stochastic processes
  • Maßtheorie
  • Stochastischer Prozess
  • Ergodentheorie
  • Wahrscheinlichkeitstheorie
  • Measure theory
  • Probabilities
  • Stochastic processes
Label
Probability, random processes, and ergodic properties, Robert M. Gray
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
428028226
Dimensions
24 cm
Edition
2nd ed.
Extent
xxxv, 322 pages
Isbn
9781441910899
Lccn
2009932896
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)428028226
Label
Probability, random processes, and ergodic properties, Robert M. Gray
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
428028226
Dimensions
24 cm
Edition
2nd ed.
Extent
xxxv, 322 pages
Isbn
9781441910899
Lccn
2009932896
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)428028226

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