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Asymptotic behavior of the supremum tail probability for anomalous diffusions

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  • Michna, Zbigniew

Abstract

In this paper we investigate asymptotic behavior of the tail probability for subordinated self-similar processes with regularly varying tail probability. We show that the tail probability of the one-dimensional distributions and the supremum tail probability are regularly varying with the pre-factor depending on the moments of the subordinating process. We can apply our result to the so-called anomalous diffusion.

Suggested Citation

  • Michna, Zbigniew, 2008. "Asymptotic behavior of the supremum tail probability for anomalous diffusions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 413-417.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:2:p:413-417
    DOI: 10.1016/j.physa.2007.09.038
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    References listed on IDEAS

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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, December.
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    Cited by:

    1. 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.

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