Small Ball Probabilities Around Random Centers of Gaussian Measures and Applications to Quantization

Steffen Dereich ()
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Steffen Dereich: Institut für Mathematik

Journal of Theoretical Probability, 2003, vol. 16, issue 2, 427-449

Abstract: Abstract Let μ be a centered Gaussian measure on a separable Hilbert space (E, ∥ ⋅ ∥). We are concerned with the logarithmic small ball probabilities around a μ-distributed center X. It turns out that the asymptotic behavior of −log μ(B(X,ε)) is a.s. equivalent to that of a deterministic function φ R (ε). These new insights will be used to derive the precise asymptotics of a random quantization problem which was introduced in a former article by Dereich, Fehringer, Matoussi, and Scheutzow.(8)

Keywords: small ball probabilites for random centers; quantization; Gaussian process (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1023578812641

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