On the exact asymptotic behaviour of the distribution of the supremum in the "critical" case
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.
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Volume (Year): 54 (2001)
Issue (Month): 4 (October)
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References listed on IDEAS
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- 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.
- Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
- Sgibnev, M. S., 2001. "Exact asymptotic behaviour of the distribution of the supremum," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 301-311, April.
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