In this paper we give a simple construction of the general stationary regenerative set, based on the stationary version of the associated subordinator (increasing Levy process). We show that, in a certain sense, the closed range of such a Levy process is a stationary regenerative subset of $\mathbb{R}$. The distribution of this regenerative set is $\sigma$-finite in general; it is finite $\operatorname{iff}$ the increments of the Levy process have finite expectation.
Publié le : 1988-07-14
Classification:
Processes with independent increments,
random sets,
stationary sets,
60D05,
60J25,
60J230
@article{1176991692,
author = {Fitzsimmons, P. J. and Taksar, Michael},
title = {Stationary Regenerative Sets and Subordinators},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1299-1305},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991692}
}
Fitzsimmons, P. J.; Taksar, Michael. Stationary Regenerative Sets and Subordinators. Ann. Probab., Tome 16 (1988) no. 4, pp. 1299-1305. http://gdmltest.u-ga.fr/item/1176991692/