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Estimates of the supremum of a class of stationary random processes

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Abstract

Under the conditions guaranteeing the uniform convergence of the spectral representations, we obtain estimates for the distribution of its supremum. We obtain estimates for the supremum of a real stationary process for which the corresponding spectral processes belong to the space\(\overline {Sub_\varphi } (\Omega )\)

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No.12, pp. 1628–1637, December, 1991.

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Éndzhirgli, M.V. Estimates of the supremum of a class of stationary random processes. Ukr Math J 43, 1515–1523 (1991). https://doi.org/10.1007/BF01066690

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Keywords

  • Stationary Process
  • Random Process
  • Spectral Representation
  • Uniform Convergence
  • Stationary Random Process