Discrete Spectrum of Nonstationary Stochastic Processes on Groups

Leonid G. Hanin and Bertram M. Schreiber

Journal of Theoretical Probability, 1998, vol. 11, issue 4, 1111-1133

Abstract: Abstract Vector-valued, asymptotically stationary stochastic processes on σ-compact locally compact abelian groups are studied. For such processes, we introduce a stationary spectral measure and show that it is discrete if and only if the asymptotically stationary covariance function is almost periodic. Using an “almost periodic Fourier transform” we recover the discrete part of the spectral measure and construct a natural, consistent estimator for the latter from samples of the process.

Keywords: Asymptotically stationary process; spectral measure; almost periodic Fourier transform (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022625117616

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