The growth rate at 0 of a Levy process is compared with the growth rate at a local minimum, $m$, of the process. For the lim inf it is found that the growth rate at $m$ is the same as that on the set of "ladder points" following 0, parameterized by inverse local time; this result gives a precise meaning to the notion that a Levy process leaves its minima "faster" than it leaves 0. A less precise result is obtained for the lim sup.
Publié le : 1981-04-14
Classification:
Stationary independent increments,
Markov process,
sample functions,
minimum,
last exit time,
local time,
60G17,
60J30,
60J25,
60G40
@article{1176994476,
author = {Millar, P. W.},
title = {Comparison Theorems for Sample Function Growth},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 330-334},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994476}
}
Millar, P. W. Comparison Theorems for Sample Function Growth. Ann. Probab., Tome 9 (1981) no. 6, pp. 330-334. http://gdmltest.u-ga.fr/item/1176994476/