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An approximation of stopped sums with applications in queueing theory

  • Miklós Csörgő (a1), Paul Deheuvels (a2) and Lajos Horváth (a3)

Abstract

We prove strong approximations for partial sums indexed by a renewal process. The obtained results are optimal. The established probability inequalities are also used to get bounds for the rate of convergence of some limit theorems in queueing theory.

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Corresponding author

Postal address: Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
∗∗ Postal address: Université Paris VI, t.45–55, E3, L.S.T.A., 4 Place Jussieu, 75230 Paris Cedex 05, France.
∗∗∗ Postal address: Bolyai Institute, Szeged University, H-6720 Szeged, Aradi vértanúk tere 1, Hungary.

Footnotes

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Research supported by an NSERC Canada grant at Carleton University.

Research done while visiting at Carleton University, also supported by NSERC Canada grants of M. Csörgő, D. A. Dawson and J. N. K. Rao.

Footnotes

References

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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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