Strongly harmonizing operators and strongly harmonizable approximations of continuous random fields on LCA groups

D. Dehay and R. Moché

Stochastic Processes and their Applications, 1988, vol. 29, issue 1, 129-139

Abstract: First we introduce a family of strongly harmonizing operators which smooth every suitably weighted continuous random field on an LCA group G into a strongly harmonizable one. Then, by means of these operators, we prove that the set of strongly harmonizable fields whose support is compact and which admit a spectral stochastic density is dense in the set of continuous random fields on G endowed with the compact convergence topology (). Finally, new sequential approximation properties of such harmonizable fields are derived when () is metrizable (e.g. G=, k or ).

Keywords: continuous; random; fields; harmonizable; random; fields; LCA; groups; spectral; stochastic; density; approximation; smoothing (search for similar items in EconPapers)
Date: 1988
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