Probabilities of Randomly Centered Small Balls and Quantization in Banach Spaces

We investigate the Gaussian small ball probabilities with random centers, find their deterministic a.s.-equivalents and establish a relation to infinite-dimensional high-resolution quantization.

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Bibliographic Details
Published in:The Annals of probability 2005-07, Vol.33 (4), p.1397-1421
Main Authors: Dereich, S., Lifshits, M. A.
Format: Article
Language:English
Subjects:
46F25
60G35
94A15
Applied sciences
asymptotic equipartition property
Banach space
Banach spaces
Covariance
Determinism
Eigenvalues
Exact sciences and technology
Functional analysis
High-resolution quantization
Hilbert spaces
Information theory
Information, signal and communications theory
Mathematical analysis
Mathematical functions
Mathematical inequalities
Mathematical models
Mathematics
Polynomials
Probabilities
Probability
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
small ball probabilities
small deviations
Stochastic processes
Studies
Telecommunications and information theory
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Description
Summary:We investigate the Gaussian small ball probabilities with random centers, find their deterministic a.s.-equivalents and establish a relation to infinite-dimensional high-resolution quantization.
ISSN:0091-1798
2168-894X
DOI:10.1214/009117905000000161