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On the supremum of an infinitely divisible process


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  • Willekens, Eric
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    It was shown by Berman in a recent paper that, for any infinitely divisible process X = {Xt, t[greater-or-equal, slanted]0} with symmetric increments, P(sup0[less-than-or-equals, slant]s[less-than-or-equals, slant]t Xs[greater-or-equal, slanted]u) ~ P(Xt[greater-or-equal, slanted]u) (u --> [infinity]) if the right tail of the Lévy measure is regularly varying with index 0

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 26 (1987)
    Issue (Month): ()
    Pages: 173-175

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    Handle: RePEc:eee:spapps:v:26:y:1987:i::p:173-175

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    Cited by:
    1. Braverman, Michael, 2000. "Suprema of compound Poisson processes with light tails," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 90(1), pages 145-156, November.
    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, Elsevier, vol. 119(1), pages 281-304, January.
    3. Braverman, Michael, 2010. "On suprema of Lévy processes with light tails," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 120(4), pages 541-573, April.
    4. Braverman, Michael, 1999. "Remarks on suprema of Lévy processes with light tailes," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 41-48, May.
    5. Braverman, Michael & Samorodnitsky, Gennady, 1995. "Functionals of infinitely divisible stochastic processes with exponential tails," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 56(2), pages 207-231, April.
    6. Tang, Qihe & Wang, Guojing & Yuen, Kam C., 2010. "Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 362-370, April.


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