Abstract
For weakly stationary random fields, conditions on coefficients of “linear dependence” are given which are, respectively, sufficient for the existence of a continuous spectral density, and necessary and sufficient for the existence of a continuous positive spectral density. For strictly stationary random fields, central limit theorems are proved under the corresponding “unrestricted ϱ-mixing” condition and just finite or “barely infinite” second moments. No mixing rate is assumed.
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Bradley, R.C. On the spectral density and asymptotic normality of weakly dependent random fields. J Theor Probab 5, 355–373 (1992). https://doi.org/10.1007/BF01046741
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DOI: https://doi.org/10.1007/BF01046741