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The supremum of a process with stationary independent and symmetric increments

Author

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  • Berman, Simeon M.

Abstract

Let Xt, t [greater-or-equal, slanted] 0, be a process with stationary independent and symmetric increments. If the tail of the Lévy spectral measure in the representation of the characteristic function is of regular variation of index -[alpha], for some 0 u) ~ P(Xt, > u), for u --> [infinity],for each t > 0.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:2:p:281-290
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    Citations

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    Cited by:

    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. 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. 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.
    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. Albin, J. M. P., 1999. "Extremes of totally skewed [alpha]-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 185-212, February.
    6. Michna, Zbigniew, 2011. "Formula for the supremum distribution of a spectrally positive [alpha]-stable Lévy process," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 231-235, February.
    7. 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.
    8. 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.

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