@article{ECP3629,
author = {Mladen Savov},
title = {On the range of subordinators},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {19},
year = {2014},
keywords = {Subordinator, Box-dimension ,Potential Measure},
abstract = {In this note we look into detail into the box-counting dimension of subordinators. Given that X is a non-decreasing Levy process which is not Compound Poisson process we show that in the limit, a.s., the minimum number of boxes of size $a$ that cover the range of $(X_s)_{s\leq t}$ is a.s. of order $t/U(a)$, where U is the potential function of X. This is a more rened result than the lower and upper index of the box-counting dimension computed by Jean Bertoin in his 1999 book, which deals with the asymptotic of the number of boxes at logarithmic scale.},
pages = {no. 84, 1-10},
issn = {1083-589X},
doi = {10.1214/ECP.v19-3629},
url = {http://ecp.ejpecp.org/article/view/3629}}