On Wiener-Hopf Factorisation and the Distribution of Extrema for Certain Stable Processes
Doney, R. A.
Ann. Probab., Tome 15 (1987) no. 4, p. 1352-1362 / Harvested from Project Euclid
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It is shown that when the index $0 < \alpha < 2, \alpha \neq 1$, and the symmetry parameter $-1 \leq \beta \leq 1$ of a stable process $\{X(t); t \geq 0\}$ are such that $P\{X(1) > 0\} = l\alpha^{-1} - k$, where $l$ and $k$ are integers, Darling's integral can be evaluated. This leads to explicit formulas for a transform of the Laplace transform of $\sup_{0\leq t\leq 1}X(t)$ and the Wiener-Hopf factors of $\{X(t), t \geq 0\}$.
Publié le : 1987-10-14
Classification:  Stable processes,  Wiener-Hopf factorisation,  supremum functional,  Levy process,  Darling's integral,  60J30 
@article{1176991981,
     author = {Doney, R. A.},
     title = {On Wiener-Hopf Factorisation and the Distribution of Extrema for Certain Stable Processes},
     journal = {Ann. Probab.},
     volume = {15},
     number = {4},
     year = {1987},
     pages = { 1352-1362},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991981}
}

Doney, R. A. On Wiener-Hopf Factorisation and the Distribution of Extrema for Certain Stable Processes. Ann. Probab., Tome 15 (1987) no. 4, pp.  1352-1362. http://gdmltest.u-ga.fr/item/1176991981/