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

Jason T. Shaw

Statistics & Probability Letters, 2004, vol. 67, issue 3, 213-220

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.

Keywords: Random; field; Spectral; density; Weakly; stationary (search for similar items in EconPapers)
Date: 2004
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