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On the density of the supremum of a stable process

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  • Kuznetsov, A.

Abstract

We study the density of the supremum of a strictly stable Lévy process. Our first goal is to investigate convergence properties of the series representation for this density, which was established recently by Hubalek and Kuznetsov (2011) [24]. Our second goal is to investigate in more detail the important case when α is rational: we derive an explicit formula for the Mellin transform of the supremum. We perform several numerical experiments and discuss their implications. Finally, we state some interesting connections that this problem has to other areas of Mathematics and Mathematical Physics and we also suggest several open problems.

Suggested Citation

  • Kuznetsov, A., 2013. "On the density of the supremum of a stable process," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 986-1003.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:3:p:986-1003
    DOI: 10.1016/j.spa.2012.11.001
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    References listed on IDEAS

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    1. Patie, P., 2009. "A few remarks on the supremum of stable processes," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1125-1128, April.
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    Cited by:

    1. Fotopoulos, Stergios & Jandhyala, Venkata & Wang, Jun, 2015. "On the joint distribution of the supremum functional and its last occurrence for subordinated linear Brownian motion," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 149-156.
    2. Coqueret, Guillaume, 2015. "On the supremum of the spectrally negative stable process with drift," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 333-340.

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