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Extremes of totally skewed [alpha]-stable processes

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  • Albin, J. M. P.

Abstract

We give upper and lower bounds for the probability for a local extrema of a totally skewed [alpha]-stable stochastic process. Often these bounds are sharp and coincide. The Gaussian case [alpha]=2 is not excluded, and there our results slightly improve existing general bounds. Applications focus on moving averages and fractional [alpha]-stable motions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:2:p:185-212
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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. Samorodnitsky, Gennady, 1988. "Extrema of skewed stable processes," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 17-39, November.
    3. Samorodnitsky, Gennady, 1991. "Probability tails of Gaussian extrema," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 55-84, June.
    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.
    5. Willekens, Eric, 1987. "On the supremum of an infinitely divisible process," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 173-175.
    6. Albin, J. M. P., 1993. "Extremes of totally skewed stable motion," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 219-224, February.
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