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Suprema of compound Poisson processes with light tails

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  • Braverman, Michael

Abstract

It is known that if the Lévy measure of a Lévy process X(t), 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1, is "heavy tailed", then the right tails of sup0[less-than-or-equals, slant]t[less-than-or-equals, slant]1X(t) and X(1) are of the same rate of decay. One of the results of this note is a description of a class of compound Poisson processes with negative drift and "light" tails (which is a subclass of Lévy processes) such that these tails are incomparable.

Suggested Citation

  • Braverman, Michael, 2000. "Suprema of compound Poisson processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 145-156, November.
    • Handle: RePEc:eee:spapps:v:90:y:2000:i:1:p:145-156
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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, 1997. "Suprema and sojourn times of Lévy processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 265-283, June.
    3. Willekens, Eric, 1987. "On the supremum of an infinitely divisible process," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 173-175.
    4. Albin, J. M. P., 1993. "Extremes of totally skewed stable motion," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 219-224, February.
    5. Braverman, Michael, 1999. "Remarks on suprema of Lévy processes with light tailes," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 41-48, May.
    6. 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.
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    1. Braverman, Michael, 2010. "On suprema of Lévy processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 541-573, April.
    2. Albin, J.M.P. & Sundén, Mattias, 2009. "On the asymptotic behaviour of Lévy processes, Part I: Subexponential and exponential processes," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 281-304, January.
    3. Braverman, Michael, 2011. "On infinitely divisible distributions with light tails of Lévy measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1648-1653, November.
    4. Braverman, Michael, 2005. "On a class of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 179-189, December.

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