On Gaussian measures in certain locally convex spaces

Balram S. Rajput

Journal of Multivariate Analysis, 1972, vol. 2, issue 3, 282-306

Abstract: The main purpose of this paper is threefold: Firstly, the topological support of Gaussian measures on certain locally convex spaces is obtained. Secondly, strongly convergent series expansions of elements in separable Fréchet spaces, related to Gaussian measures, are obtained; this result is applied to obtain Karhunen-Loève-type expansions for Gaussian processes. Thirdly, it is shown that any zero-mean Gaussian measure on a separable Fréchet space can be obtained as the [sigma] extension of the canonical Gaussian cylinder measure of a separable Hilbert space. Other related problems are also discussed.

Keywords: Gaussian; measure; Gaussian; process; Karhunen-Loeve; expansion; topological; support; characteristic; function; locally; convex; space; Frechet; space (search for similar items in EconPapers)
Date: 1972
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