Geodesic
On a maximum of stable L\'evy processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 380-386

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Let $G$ and $S$ be the location and the maximal value of a stable Lévy process $X$ on an interval $[0,a]$. It is shown that the dimensionless $S/G^h$, where h is the self-similarity parameter of $X$, is independent of $G$. This fact allows us to analyze $G$ for the trajectories of $X$ with high and low maxima.
Keywords: extremal values, Lévy processes, self-similar processes. 
@article{TVP_2000_45_2_a11,
     author = {G. M. Molchan},
     title = {On a maximum of stable {L\'evy} processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {380--386},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a11/}
}
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G. M. Molchan. On a maximum of stable L\'evy processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 380-386. http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a11/