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Ukrainian Mathematical Journal

, Volume 50, Issue 4, pp 533–538 | Cite as

A limit theorem for mixing processes subject to rarefaction. I

  • V. O. Gasanenko
Article
  • 12 Downloads

Abstract

We prove a limit theorem on the approximation of point mixing processes subject to rarefaction by general renewal processes. This theorem contains a weaker condition on the mixing coefficient than the known conditions.

Keywords

Limit Theorem Limit Point Weak Convergence Renewal Process Mathematical Expectation 
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References

  1. 1.
    V. A. Gasanenko, “Processes subject to rarefaction,” Ukr. Mat. Zh., 35, No. 1, 27–30 (1983).CrossRefMathSciNetGoogle Scholar
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    P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).MATHGoogle Scholar
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    A. A. Borovkov, “Convergence of measures and random processes,” Usp. Mat. Nauk, 31, No. 2, 3–68 (1976).MathSciNetGoogle Scholar
  4. 4.
    V. V. Anisimov, Random Processes with Discrete Component. Limit Theorems [in Russian], Kiev, Vyshcha Shkola (1988).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. O. Gasanenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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