White Noise Representation of Gaussian Random Fields

2012/01/26 by Gelbaum, Zachary
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1201.5635

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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