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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0290444-6
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0290444-6
Keywords: Gaussian random measure, equivalence of probability measures, covariance function, factorable
Article copyright: © Copyright 1972 American Mathematical Society

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