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Extremes

, Volume 7, Issue 4, pp 337–365 | Cite as

Tail Calculus with Remainder, Applications to Tail Expansions for Infinite Order Moving Averages, Randomly Stopped Sums, and Related Topics

  • Ph. Barbe
  • W. P. McCormick
Article

Abstract

We derive asymptotic expansions for tails of infinite weighted convolutions of some heavy-tailed distributions. Applications are given to tail expansion of the marginal distribution of ARMA processes, randomly stopped sums, as well as limiting waiting time distribution.

Key words

asymptotic expansion convolution heavy tail infinite order moving averages limiting waiting time distribution randomly stopped sums 

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References

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.CNRSParisFrance
  2. 2.Department of StatisticsUniversity of GeorgiaAthensUSA

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