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Stationary processes for translation operators.

Research output: Contribution to journalJournal article

Published

<mark>Journal publication date</mark>1996
<mark>Journal</mark>Proceedings of the London Mathematical Society
Issue3
Volume72
Number of pages24
Pages697-720
<mark>Original language</mark>English

Abstract

We consider the class of gaussian processes on complete manifolds of bounded curvature which are stationary under the generalised translation operation generated by the Laplace–Beltrami operator. We give a sufficient condition on the spectral density for the sample paths to be almost surely continuous. We provide a sufficient condition for a positive definite function on X x X to be the covariance function of a stationary process.