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Stationary Processes for Translation Operators
Author(s) -
Blower G.
Publication year - 1996
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-72.3.697
Subject(s) - mathematics , translation (biology) , stationary process , operator (biology) , covariance , bounded function , laplace transform , gaussian , function (biology) , mathematical analysis , curvature , pure mathematics , gaussian process , statistics , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , evolutionary biology , biology , messenger rna , transcription factor , gene
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 to be the covariance function of a stationary process.
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