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Cybernetics and Systems Analysis

, Volume 55, Issue 5, pp 772–777 | Cite as

Large Deviations of Empirical Estimates in the Stochastic Programming Problem with Nonstationary Observations and Continuous Time

  • P. S. KnopovEmail author
  • E. J. Kasitskaya
Article
  • 5 Downloads

Abstract

The paper considers a stochastic programming problem with the empirical function constructed based on nonstationary observations and continuous time. A random process, stationary in a narrow sense and satisfying the strong mixing condition is investigated in the problem. The conditions under which the empirical estimate is consistent are given and large deviations of the estimate are considered.

Keywords

stochastic programming problem stationary ergodic random process strong mixing condition large deviations 

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References

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    P. Knopov and E. Kasitskaya, “Large deviations for the method of empirical means in stochastic optimization problems with continuous time observations,” in: S. Butenko, P. M. Pardalos, and V. Shylo (eds.), Optimization Methods and Applications. In Honor of the 80-th Birthday of Ivan V. Sergienko, Springer, New York (2017), pp. 263–275.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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