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Asymptotics of supremum distribution of [alpha](t)-locally stationary Gaussian processes

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  • De[combining cedilla]bicki, Krzysztof
  • Kisowski, Pawel

Abstract

We study the exact asymptotics of , as u-->[infinity], for centered Gaussian processes with the covariance function satisfying as h-->0. The obtained results complement those already considered in the literature for the case of locally stationary Gaussian processes in the sense of Berman, where [alpha](t)[reverse not equivalent][alpha]. It appears that the behavior of [alpha](t) in the neighborhood of its global minimum on [0,S] significantly influences the asymptotics. As an illustration we work out the case of X(t) being a standardized multifractional Brownian motion.

Suggested Citation

  • De[combining cedilla]bicki, Krzysztof & Kisowski, Pawel, 2008. "Asymptotics of supremum distribution of [alpha](t)-locally stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2022-2037, November.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:11:p:2022-2037
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    References listed on IDEAS

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    1. Hüsler, J. & Piterbarg, V., 2004. "On the ruin probability for physical fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 315-332, October.
    2. Hüsler, J. & Piterbarg, V., 1999. "Extremes of a certain class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 257-271, October.
    3. Dieker, A.B., 2005. "Extremes of Gaussian processes over an infinite horizon," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 207-248, February.
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    Cited by:

    1. Bai, Long, 2020. "Extremes of standard multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 159(C).

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