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Cramer's estimate for Lévy processes

Author

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  • Bertoin, J.
  • Doney, R. A.

Abstract

It is shown that the usual method of establishing Cramer's estimate also works for Lévy processes.

Suggested Citation

  • Bertoin, J. & Doney, R. A., 1994. "Cramer's estimate for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 363-365, December.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:5:p:363-365
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    Citations

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    Cited by:

    1. J'er^ome Spielmann, 2017. "Classification of the Bounds on the Probability of Ruin for L{\'e}vy Processes with Light-tailed Jumps," Papers 1709.10295, arXiv.org, revised Feb 2018.
    2. Asghari, N.M. & Dȩbicki, K. & Mandjes, M., 2015. "Exact tail asymptotics of the supremum attained by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 180-184.
    3. Chaumont, Loïc & Rivero, Víctor, 2007. "On some transformations between positive self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1889-1909, December.
    4. Mijatović, Aleksandar & Pistorius, Martijn, 2015. "Buffer-overflows: Joint limit laws of undershoots and overshoots of reflected processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2937-2954.
    5. Arista, Jonas & Rivero, Víctor, 2023. "Implicit renewal theory for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 262-287.
    6. Palmowski, Zbigniew & Pistorius, Martijn, 2009. "Cramér asymptotics for finite time first passage probabilities of general Lévy processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1752-1758, August.
    7. Baurdoux, E.J. & Palmowski, Z. & Pistorius, M.R., 2017. "On future drawdowns of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2679-2698.
    8. Griffin, Philip S. & Maller, Ross A. & Schaik, Kees van, 2012. "Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 382-392.
    9. Boxma, Onno & Kella, Offer & Mandjes, Michel, 2023. "On fluctuation-theoretic decompositions via Lindley-type recursions," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 316-336.
    10. Fotopoulos, Stergios & Jandhyala, Venkata & Wang, Jun, 2015. "On the joint distribution of the supremum functional and its last occurrence for subordinated linear Brownian motion," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 149-156.
    11. Griffin, Philip S., 2020. "General tax structures for a Lévy insurance risk process under the Cramér condition," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1368-1387.
    12. Griffin, Philip S. & Roberts, Dale O., 2016. "Sample paths of a Lévy process leading to first passage over high levels in finite time," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1331-1352.
    13. Irmina Czarna & Zbigniew Palmowski, 2010. "Ruin probability with Parisian delay for a spectrally negative L\'evy risk process," Papers 1003.4299, arXiv.org, revised Apr 2010.
    14. Griffin, Philip S., 2022. "Path decomposition of a reflected Lévy process on first passage over high levels," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 29-47.
    15. Korshunov, Dmitry, 2018. "On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1316-1332.
    16. Jérôme Spielmann, 2018. "Classification of the Bounds on the Probability of Ruin for Lévy Processes with Light-tailed Jumps," Working Papers hal-01597828, HAL.
    17. Griffin, Philip S. & Maller, Ross A. & Roberts, Dale, 2013. "Finite time ruin probabilities for tempered stable insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 478-489.
    18. Palmowski, Zbigniew & Vlasiou, Maria, 2011. "A Lévy input model with additional state-dependent services," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1546-1564, July.

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