@article{ECP2757,
author = {Daniel Hackmann and Alexey Kuznetsov},
title = {A note on the series representation for the density of the supremum of a stable process},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {18},
year = {2013},
keywords = {stable processes, supremum, Mellin transform, continued fractions},
abstract = {An absolutely convergent double series representation for the density of the supremum of $\alpha$-stable Lévy process was obtained by Hubalek and Kuznetsov for almost all irrational $\alpha$. This result cannot be made stronger in the following sense: the series does not converge absolutely when $\alpha$ belongs to a certain subset of irrational numbers of Lebesgue measure zero. Our main result in this note shows that for every irrational $\alpha$ there is a way to rearrange the terms of the double series, so that it converges to the density of the supremum. We show how one can establish this stronger result by introducing a simple yet non-trivial modification in the original proof of Hubalek and Kuznetsov.},
pages = {no. 42, 1-5},
issn = {1083-589X},
doi = {10.1214/ECP.v18-2757},
url = {http://ecp.ejpecp.org/article/view/2757}}