Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
By Alexey Kuznetsov, Juan Carlos Pardo. 2010
87 citations recorded by the source corpus.
We study the distribution and various properties of exponential functionals of hypergeometric Lévy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applications we present a new proof of some of the results on the density of the supremum of a stable process, which were recently obtained in Hubalek and Kuznetsov (Electron. Commun. Probab. 16:84–95, 2011) and Kuznetsov (Ann. Probab. 39(3):1027–1060, 2011). We also derive several new results related to (i) the entrance law of a stable process conditioned to stay positive, (ii) the entrance law of the excursion measure of a stable process reflected at its past infimum, (iii) the distribution of the lifetime of a stable process conditioned to hit zero continuously and (iv) the entrance law and the last passage time of the radial part of a multidimensional symmetric stable process.
Subfields: Finance, Management Information Systems, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b4d5dc4629c25597fb070a20d69aa7cc1da4e034
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Citations in the corpus
- Bernstein-gamma functions and exponential functionals of Levy Processes (2016, background): “For particular subclasses, that include and allow the study of the supremum of the stable process, this transform has been evaluated and sometimes via inversion the law of exponential functional has been obtained, see [8, 56, 40, 42].”