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On a class of Lévy processes

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  • Braverman, Michael

Abstract

A class of Lévy processes with exponentially decaying tails of Lévy measure are investigated. One of the results is that the probability tails of the supremum of the process over finite interval and of the value of the process at the right end of the interval have equivalent probability tails.

Suggested Citation

  • Braverman, Michael, 2005. "On a class of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 179-189, December.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:3:p:179-189
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    References listed on IDEAS

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    1. 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.
    2. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    3. Braverman, Michael, 2000. "Suprema of compound Poisson processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 145-156, November.
    4. 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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    Cited by:

    1. 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.
    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.

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    Keywords

    Lévy processes Tails Extremes;

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