Stationary processes for translation operators.

Blower, G. (1996) Stationary processes for translation operators. Proceedings of the London Mathematical Society, 72 (3). pp. 697-720. ISSN 1460-244X

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.