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On Large Deviations of Gaussian Measures in Banach Spaces

  • Marek Slaby
Chapter
Part of the Progress in Probability book series (PRPR, volume 30)

Abstract

Throughout this paper E will denote a separable Banach space and γ will be a full centered Gaussian measure on E. Define an operator S: E’E by S f = ∫ x f(x)γ(dx), and a scalar product <, >γ on SE’ by
$$ <Sf,Sg>_\gamma =\int f(x)g(x)\gamma(dx) $$
The completion of S E’ with respect to the norm ∥x;∥γ = √<x,x >γ is denoted by Hγ and called the reproducing kernel Hilbert space of γ. Since
$$||Sf||\leq _{||g||E^{*}\leq1}^<Superscript>p</Superscript>[\int g^{2}(x)\gamma(dx)]^{1/2}\cdot ||Sf||_{\gamma} $$
can and will be viewed as a subset of E. For details on the construction and properties of the reproducing kernel Hilbert space we refer the reader to [2] or [5].

Keywords

Banach Space Random Vector Moderate Deviation Gaussian Measure Reproduce Kernel Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Marek Slaby
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of Nebraska - LincolnLincolnUSA

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