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On the exact asymptotic behaviour of the distribution of the supremum in the "critical" case

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  • Sgibnev, M. S.

Abstract

We consider a random walk drifting to -[infinity] with distribution F of the steps. The paper considers the exact asymptotic behaviour of the distribution D of the supremum when there exists [gamma]>0 such that and , thus filling the remaining gap in describing the behaviour of D in terms of -distributions.

Suggested Citation

  • Sgibnev, M. S., 2001. "On the exact asymptotic behaviour of the distribution of the supremum in the "critical" case," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 357-362, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:357-362
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    References listed on IDEAS

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    1. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    2. Sgibnev, M. S., 2001. "Exact asymptotic behaviour of the distribution of the supremum," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 301-311, April.
    3. Veraverbeke, N., 1977. "Asymptotic behaviour of Wiener-Hopf factors of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 27-37, February.
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