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Two-side estimates of geometric convolutions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1546)

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  • Markov Chain
  • Regenerative Model
  • High Moment
  • Renewal Theory
  • Queueing Model

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References

  1. M. Brown, Error bounds for exponential approximation of geometric convolutions, Ann. Probab., 18 (1990), pp. 1388–1402.

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  2. D. J. Daley, Tight bounds for the renewal function of a random walk, Ann. Probab., 8 (1980), pp. 615–621.

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  3. E. B. Dynkin, Markov Processes, vol I, II, Spinger, Berlin, 1965.

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  4. V. V. Kalashnikov, Quilitative Analysis of Complex Sistems Behaviou by Trial Functions Method, Nauka, Moscow, 1978. (In Russian.)

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  5. V. V. Kalashnikov and S. T. Rachev, Mathematical Methods for Constructing of Queueing Models, Wadsnorth and Brooks, Cole, 1990.

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  6. V. V. Kalashnikov and S. Yu. Vsekhsviatskii, Metric estimates of the first occurrence time in regenerative processes, Lect. Notes Math., Springer, 1155 (1985), pp. 193–208.

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  7. V. V. Kalashnikov and S. Yu. Vsekhsviatskii, Estimates in the Renyi's theorem in terms of renewal theory, Probab. Theory Appl., 33 (1988), pp. 369–373.

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  8. V. V. Kalashnikov and S. Yu. Vsekhsviatskii, On the connection of Renyi's theorem and renewal theory, Lect. Notes Math., Springer, 1412 (1989), pp. 83–102.

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  9. G. Lorden, On excess over the boundary, Ann. Math. Stat., 41 (1970), pp. 520–527.

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© 1993 Springer-Verlag

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Kalashnikov, V.V. (1993). Two-side estimates of geometric convolutions. In: Kalashnikov, V.V., Zolatarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1546. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084484

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  • DOI: https://doi.org/10.1007/BFb0084484

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  • Print ISBN: 978-3-540-56744-8

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