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On the spectral density and asymptotic normality of weakly dependent random fields
Authors:Richard C Bradley
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
Abstract:For weakly stationary random fields, conditions on coefficients of ldquolinear dependencerdquo 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 ldquounrestricted rhov-mixingrdquo condition and just finite or ldquobarely infiniterdquo second moments. No mixing rate is assumed.
Keywords:Stationary random fields  spectral density  rhov-mixing" target="_blank">gif" alt="rhov" align="MIDDLE" BORDER="0">-mixing  central limit theorem
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