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A limit theorem for mixing processes subject to rarefaction. II

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Abstract

The limit theorem proved in the first part of this paper is applied to the well-known schemes of processes subject to rarefaction arising in queuing theory, mathematical biology, and in problems for counters.

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References

  1. V. A. Gasanenko, “Applications of thinning processes,” Ann. Univ. Sci. Budapest. Sec. Comp., 11, 35–51 (1991).

    MathSciNet  Google Scholar 

  2. Yu. K. Belyaev, “Limit theorems for processes subject to rarefaction,” Teor. Ver. Primen., 8, No. 2, 175–184 (1963).

    MathSciNet  Google Scholar 

  3. R. Coleman and J. L. Gastwirth, “Some models for interaction of renewal processes related to neuron firing,” J. Appl. Probab., 6, 38–58 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  4. T. Hoopen and H. Reuver, “Selective interaction of two independent recurrent processes,” J. Appl. Probab., 2, 286–292 (1965).

    Article  MATH  Google Scholar 

  5. P. Jagers and T. Lindwall, “Thinning and rare events in point processes,” Z. Wahrscheinlichketstheor. verw. Geb., 28, 89–98 (1974).

    Article  MATH  Google Scholar 

  6. I. A. Ibragimov, “Limit theorems for stationary processes,” Teor. Ver. Primen., 4, No. 4, 361–392 (1984).

    Google Scholar 

  7. P. Billingsley, Convergence of Probability Measures [Russian translation], Nauka, Moscow (1977).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 603–612, May, 1998.

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Gasanenko, V.O. A limit theorem for mixing processes subject to rarefaction. II. Ukr Math J 50, 685–696 (1998). https://doi.org/10.1007/BF02514322

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  • DOI: https://doi.org/10.1007/BF02514322

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