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Remarks on suprema of Lévy processes with light tailes

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  • Braverman, Michael

Abstract

Let X(t), 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1 be a Lévy process. A comparison between the right tail of sup0[less-than-or-equals, slant]t[less-than-or-equals, slant]1 X(t) and the right tail of X(1) is considered. An example is given for which these tailes are incomparable. A class of Lévy process with "light" tails is described for which these tails have the same behavior.

Suggested Citation

  • Braverman, Michael, 1999. "Remarks on suprema of Lévy processes with light tailes," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 41-48, May.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:1:p:41-48
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    References listed on IDEAS

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    1. Berman, Simeon M., 1986. "The supremum of a process with stationary independent and symmetric increments," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 281-290, December.
    2. Braverman, Michael & Samorodnitsky, Gennady, 1995. "Functionals of infinitely divisible stochastic processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 207-231, April.
    3. Braverman, Michael, 1997. "Suprema and sojourn times of Lévy processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 265-283, June.
    4. Willekens, Eric, 1987. "On the supremum of an infinitely divisible process," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 173-175.
    5. Albin, J. M. P., 1993. "Extremes of totally skewed stable motion," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 219-224, February.
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    Cited by:

    1. Braverman, Michael, 2000. "Suprema of compound Poisson processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 145-156, November.

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