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Probability Distributions on Banach Spaces

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathe...

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Bibliographic Details
Main Authors: Vakhania, N., Tarieladze, Vazha (Author), Chobanyan, S. (Author)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1987, 1987
Edition:1st ed. 1987
Series:Mathematics and its Applications, Soviet Series
Subjects:
Mathematical Analysis
Statistics 
Analysis
Statistics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. Measurability and Measures
  • 1. ?-algebras and measurable mappings in metric space
  • 2. ?-algebras in Banach spaces
  • 3. Probability measures on topological spaces
  • 4. The semigroup of probability measures
  • 5. Invariant and quasi-invariant measures. Scalarly non-degenerate measures
  • Supplementary comments
  • II. Measures and Random Elements. Weak and Strong Orders
  • 1. Random elements
  • 2. Weak and strong orders of random elements
  • 3. The expectation
  • 4. Conditional expectations, martingales and connections with the Radon-Nikodym Property
  • Supplementary comments
  • III. Covariance Operators
  • 1. Operators mapping spaces into their duals
  • 2. Covariance operators
  • Supplementary comments
  • IV. Characteristic Functionals
  • 1. Positive-definite functions
  • 2. Definition and general properties of characteristic functionals
  • 3. Characteristic functionals and weak convergence
  • 4. Bochner’s theorem
  • Supplementary comments
  • V. Sums of Independent Random Elements
  • 1. Independent random elements
  • 2. Series of independent random elements
  • 3. Integrability of sums and the mean convergence of random series
  • 4. Comparison of random series
  • 5. Some special series
  • 6. Random series in spaces which do not contain c0
  • Supplementary comments
  • VI. Topological Description of Characteristic Functionals and Cylindrical Measures
  • 1. Sazonov’s theorem and related topics
  • 2. Necessary and sufficient topologies. Spaces with the Sazonov property
  • 3. Cylindrical measures
  • 4. The case of locally convex spaces. Minlos’ theorem
  • 5. Radonifying operators
  • Supplementary comments

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