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

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  • Shaw, Jason T.
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4BMJ9RR-5/2/0a498ea5998a6d07e1ca2f359ae450ed
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 67 (2004)
    Issue (Month): 3 (April)
    Pages: 213-220

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    Handle: RePEc:eee:stapro:v:67:y:2004:i:3:p:213-220

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    Keywords: Random field Spectral density Weakly stationary;

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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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