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Refining the exponential asymptotic expansion for the distribution function of a sum of a random number of nonnegative random variables

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References

  1. B. V. Gnedenko and I. N. Kovalenko, Introduction to Queueing Theory [in Russian], Nauka, Moscow (1987).

    MATH  Google Scholar 

  2. A. D. Solov'ev, “Asymptotic behavior of the moment of a rare event in a regenerative process,” Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 6, 79-89 (1971).

  3. I. N. Kovalenko, Studies in Reliability Analysis of Complex Systems [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  4. I. N. Kovalenko, Analysis of Rare Events for Estimation of Reliability and Efficiency of Complex Systems [in Russian], Sovetskoe Radio, Moscow (1980).

    Google Scholar 

  5. V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications [in Russian], Naukova Dumka, Kiev (1976).

    MATH  Google Scholar 

  6. V. S. Korolyuk and A. F. Turbin, Mathematical Principles of Phase-Space Aggregation of Complex Systems [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  7. V. V. Anisimov, Stochastic Processes with a Discrete Component. Limit Theorems [in Russian], Vishcha Shkola, Kiev (1988).

    MATH  Google Scholar 

  8. V. V. Kalashnikov, Qualitative Analysis of the Behavior of Complex Systems by Test Function Method [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  9. A. D. Solov'ev and O. Sakhobov, “Two-sided reliability bounds of systems with repair,” Izv. Akad. Nauk UzbSSR, ser. Phys.-Math. Sci., No. 5, 28–33 (1967).

  10. V. D. Shpak and L. S. Stoikova, “Two-sided bounds for the distribution function of stopping time of generalized transient renewal process with an exponentially distributed component,” Kibernetika, No. 2, 122–123 (1985).

  11. S. Yu. Vsekhsvyatskii and V. V. Kalashnikov, “Bounds in the Renyi theorem in terms of renewal theory,” Teor. Veroyat. Primen.,33, No. 2, 369–373 (1988).

    Google Scholar 

  12. N. V. Kartashov, “Inequalities in the Renyi theorem,” Teor. Veroyat. Mat. Stat., No. 45, 27–33 (1991).

  13. A. N. Nakonechnyi, “Refinement of the Renyi theorem,” Kibern. Sist. Anal., No. 6, 170–171 (1993).

  14. W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation], Vol. 2, Mir, Moscow (1984).

    Google Scholar 

  15. V. D. Shpak, “Estimating the stopping probability of a regeneration process in a fixed time by Monte Carlo method,” Kibernetika, No. 1, 75–79 (1983).

  16. P. Embrechts and K. Kluppelberg, “Some aspects of insurance mathematics,” Teor. Veroyat. Primen.,38, No. 2, 374–417 (1993).

    MATH  Google Scholar 

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Authors
  1. A. N. Nakonechnyi
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The research described in this publication was made possible in part by grant No. UAL200 from the Joint Fund of the Government of Ukraine and International Science Foundation.

Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 112–121, January–February, 1997.

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Nakonechnyi, A.N. Refining the exponential asymptotic expansion for the distribution function of a sum of a random number of nonnegative random variables. Cybern Syst Anal 33, 89–96 (1997). https://doi.org/10.1007/BF02665946

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  • DOI: https://doi.org/10.1007/BF02665946

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