Rootzen (1978) gives a sufficient condition for sample continuity of moving average processes with respect to stable motion with index $\alpha$ less than two. We provide a simple proof of this criterion for $\alpha < 1$ and show that the condition is then also necessary for continuity of the process. The same result holds for the moving-maximum process. A description of the local behaviour of the sample functions of such processes is given.
Publié le : 1988-01-14
Classification:
Moving average,
stable,
max stable,
stationary,
a.s. continuity,
60G10,
60G17
@article{1176991905,
author = {Balkema, A. A. and Haan, L. De},
title = {Almost Sure Continuity of Stable Moving Average Processes with Index Less Than One},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 333-343},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991905}
}
Balkema, A. A.; Haan, L. De. Almost Sure Continuity of Stable Moving Average Processes with Index Less Than One. Ann. Probab., Tome 16 (1988) no. 4, pp. 333-343. http://gdmltest.u-ga.fr/item/1176991905/