White Noise Representation of Gaussian Random Fields

Zachary Gelbaum

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arXiv · 1201.5635

White Noise Representation of Gaussian Random Fields

Zachary Gelbaum

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Abstract

We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a Gaussian random field indexed by a compact measure space. As an application we show how existing theory for integration with respect to Gaussian processes indexed by $[0,1]$ can be extended to Gaussian fields indexed by compact measure spaces.

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Zachary Gelbaum. 2012-01-26. White Noise Representation of Gaussian Random Fields. https://arxiv.org/abs/1201.5635

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