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Article overview
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Fluctuations of stable processes and exponential functionals of hypergeometric Levy processes | | Alexey Kuznetsov
; Juan Carlos Pardo
; | | Date: |
3 Dec 2010 | | Abstract: | We study the distribution and various properties of exponential functionals
of hypergeometric Levy 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 by Kuznetsov "On extrema of stable
processes" (2010) and Hubalek and Kuznetsov "A convergent series representation
for the density of the supremum of a stable process" (2010). We also derive
some new results related to (i) the entrance law of the stable process
conditioned to stay positive, (ii) the entrance law of the excursion measure of
the stable process reflected at its past infimum and (iii) the entrance law and
the last passage time of the radial part of n-dimensional symmetric stable
process. | | Source: | arXiv, 1012.0817 | | Services: | Forum | Review | PDF | Favorites | |
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