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Random fields and the limit of their spectral densities: existence and bounds

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  • Shaw, Jason T.

Abstract

For a sequence of discrete random fields indexed by an integer lattice of finite dimension that satisfy a weak linear dependence condition, have converging covariances, and (not necessarily continuous) spectral densities f(l) bounded between two positive constants, a limiting spectral density f bounded between two positive constants is obtained, along with a weak form of convergence of f(l) to f. Two examples are given that show this convergence seems to be the best one can get.

Suggested Citation

  • Shaw, Jason T., 2004. "Random fields and the limit of their spectral densities: existence and bounds," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 213-220, April.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:3:p:213-220
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    References listed on IDEAS

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    1. Bradley, Richard C., 2003. "A criterion for a continuous spectral density," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 108-125, July.
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