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On suprema of Lévy processes with light tails

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  • Braverman, Michael

Abstract

Let X(t),t>=0,X(0)=0, be a Lévy process with a spectral Lévy measure [rho]. Assuming that and the right tail of [rho] is light, we show that in the presence of the Brownian component as u-->[infinity], while in the absence of a Brownian component these tails are not always comparable.

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  • Braverman, Michael, 2010. "On suprema of Lévy processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 541-573, April.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:4:p:541-573
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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, 2000. "Suprema of compound Poisson processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 145-156, November.
    3. 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.
    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. & 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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    1. Braverman, Michael, 2011. "On infinitely divisible distributions with light tails of Lévy measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1648-1653, November.

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