A criterion for a continuous spectral density

Authors:
Richard C. Bradley
Affiliations:
Department of Mathematics, Indiana University, Bloomington, IN
Venue:
Journal of Multivariate Analysis
Year:
2003

Citing 3
Cited 1

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A continuous spectral density for a random field of continuous-index

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Abstract

For a given weakly stationary random field indexed by the integer lattice of an arbitrary finite dimension, a necessary and sufficient condition is given for the existence of a continuous spectral density. The condition involves the covariances of pairs of sums of the random variables, with the two index sets being "separated" from each other (but possibly "interlaced") by a certain distance along a coordinate direction.