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Cramer's estimate for Lévy processes

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Author Info

  • Bertoin, J.
  • Doney, R. A.
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    Abstract

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

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-45DB13G-4/2/c8ac3337b681bd46b0c1ba99f1df191e
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 21 (1994)
    Issue (Month): 5 (December)
    Pages: 363-365

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    Handle: RePEc:eee:stapro:v:21:y:1994:i:5:p:363-365

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    Cited by:
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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