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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the equivalence of Gaussian processes with factorable covariance functions

Author: W. J. Park
Journal: Proc. Amer. Math. Soc. 32 (1972), 275-279
MSC: Primary 60.40
MathSciNet review: 0290444
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Abstract: Let $ {\{ {X_t}\} _{t \in T}}$ be a Gaussian process on a probability space $ (\Omega ,\mathcal{F},P)$ with a factorable covariance function. We assume here that T is a p-dimensional Euclidean space. The purpose of this paper is to give necessary and sufficient conditions that a probability measure Q with respect to which $ {\{ {X_t}\} _{t \in T}}$ is a Gaussian process is equivalent to a probability measure P.

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Keywords: Gaussian random measure, equivalence of probability measures, covariance function, factorable
Article copyright: © Copyright 1972 American Mathematical Society

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