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Stationary processes for translation operators.

Research output: Contribution to journalJournal article


Journal publication date1996
JournalProceedings of the London Mathematical Society
Number of pages24
Original languageEnglish


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.