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Discrete Spectrum of Nonstationary Stochastic Processes on Groups

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  • Leonid G. Hanin
  • Bertram M. Schreiber

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.

Suggested Citation

  • Leonid G. Hanin & Bertram M. Schreiber, 1998. "Discrete Spectrum of Nonstationary Stochastic Processes on Groups," Journal of Theoretical Probability, Springer, vol. 11(4), pages 1111-1133, October.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:4:d:10.1023_a:1022625117616
    DOI: 10.1023/A:1022625117616
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    References listed on IDEAS

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    1. Hurd, Harry L., 1991. "Correlation theory of almost periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 24-45, April.
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