On the spectral density and asymptotic normality of weakly dependent random fields |
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Authors: | Richard C Bradley |
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Institution: | (1) Department of Mathematics, Indiana University, 47405 Bloomington, Indiana;(2) Center for Stochastic Processes, Department of Statistics, University of North Carolina, 27599 Chapel Hill, North Carolina |
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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 -mixing condition and just finite or barely infinite second moments. No mixing rate is assumed. |
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Keywords: | Stationary random fields spectral density -mixing" target="_blank">gif" alt="rhov" align="MIDDLE" BORDER="0">-mixing central limit theorem |
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