On the density of the supremum of a stable process

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Kuznetsov, A.

关键词: Stable process;    Supremum;    q-series;    q-Pochhammer symbol;    Continued fractions;    Diophantine approximations;    Double gamma function;    Barnes function;    Dilogarithm;    Quantum dilogarithm;   

DOI  :  10.1016/j.spa.2012.11.001

来源: Elsevier

【 摘 要 】

We study the density of the supremum of a strictly stable Levy 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 a 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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free