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Distribution tails of sample quantiles and subexponentiality

Author

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  • Braverman, Michael
  • Samorodnitsky, Gennady

Abstract

We show that subexponentiality is not sufficient to guarantee that the distribution tail of a sample quantile of an infinitely divisible process is equivalent to the "tail" of the same sample quantile under the corresponding Lévy measure. However, such an equivalence result is shown to hold under either an assumption of an appropriately slow tail decay or an assumption on the structure of the process.

Suggested Citation

  • Braverman, Michael & Samorodnitsky, Gennady, 1998. "Distribution tails of sample quantiles and subexponentiality," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 45-60, August.
    • Handle: RePEc:eee:spapps:v:76:y:1998:i:1:p:45-60
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    References listed on IDEAS

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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    2. Miura, Ryozo, 1992. "A Note on Look-Back Options Based on Order Statistics," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 27(1), pages 15-28, November.
    3. Embrechts, Paul & Samorodnitsky, Gennady, 1995. "Sample quantiles of heavy tailed stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 217-233, October.
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