Large-deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution

@inproceedings{Korshunov1998LargedeviationPF,
  title={Large-deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution},
  author={D. Korshunov},
  year={1998}
}
Abstract. We consider the sums Sn = ξ1 + · · · + ξn of independent identically distributed random variables with negative mean value. In the case of subexponential distribution of the summands, the asymptotic behavior is found for the probability of the event that the maximum of sums max(S1, . . . , Sn) exceeds high level x. The asymptotics obtained describe this tail probability uniformly with respect to all values of n. 

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References

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Showing 1-10 of 12 references

On the distribution of the maxima of partial sums

  • M. S. Sgibnev
  • Statist. Probab. Lett., 28
  • 1996
1 Excerpt

Subexponential distributions and integrated tails

  • C. Klüppelberg
  • J. Appl. Probab., 25
  • 1988
2 Excerpts

A problem on large deviations in a space of trajectories

  • I. F. Pinelis
  • Theory Probab. Appl., 26
  • 1981
3 Excerpts

On the distribution of the maxima of partial sums , Statist

  • M. S. Sgibnev
  • Probab . Lett .
  • 1981

Subexponentiality and infinite divisibility

  • P. Embrechts, C. M. Goldie, N. Veraverbeke
  • Z. Wahrsch. Verw. Gebiete, 49
  • 1979
1 Excerpt

Probabilities of large deviations for sums of independent random variables attracted to a stable law

  • V. V. Godovanchuk
  • Theory Probab. Appl., 23
  • 1978
2 Excerpts

Asymptotic behavior of Wiener–Hopf factors of a random walk

  • N. Veraverbeke
  • Stochastic Process. Appl., 5
  • 1977
1 Excerpt

Asymptotic behavior of Wiener – Hopf factors of a random walk , Stochastic Process

  • N. Veraverbeke
  • Appl .
  • 1975

The class of subexponential distributions

  • J. L. Teugels
  • Ann. Probab., 3
  • 1975
1 Excerpt

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