Consistency and Properties of Large Deviations of Empirical Estimates in Stochastic Optimization Problems for Homogeneous Random Fields under Nonhomogeneous and Homogeneous Observations

Abstract

The paper considers a stochastic programming problem with the empirical function constructed from nonhomogeneous observations of a homogeneous random field. The field satisfying the strong mixing condition is investigated in the problem. The conditions whereby the empirical estimate is consistent are given, and large deviations of the estimate for homogeneous observations are estimated.

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Correspondence to P. S. Knopov.

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The study was financially supported by the grant 2020.02/0121 of the National Research Foundation of Ukraine.

Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2021, pp. 21–34.

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Knopov, P.S., Kasitskaya, E.J. Consistency and Properties of Large Deviations of Empirical Estimates in Stochastic Optimization Problems for Homogeneous Random Fields under Nonhomogeneous and Homogeneous Observations. Cybern Syst Anal 57, 16–29 (2021). https://doi.org/10.1007/s10559-021-00326-0

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Keywords

  • stochastic programming problem
  • random field homogeneous in a strict sense
  • nonhomogeneous observations
  • strong mixing condition
  • large deviations