On the density of the supremum of a stable process

A. Kuznetsov

Stochastic Processes and their Applications, 2013, vol. 123, issue 3, 986-1003

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.

Keywords: Stable process; Supremum; q-series; q-Pochhammer symbol; Continued fractions; Diophantine approximations; Double gamma function; Barnes function; Dilogarithm; Quantum dilogarithm (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:3:p:986-1003

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DOI: 10.1016/j.spa.2012.11.001

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