Bravo: Local extinction in continuous-state branching processes with immigration

The purpose of this article is to observe that the zero sets of continuous-state branching processes with im-migration (CBI) are infinitely divisible regenerative sets. Indeed, they can be constructed by the procedure of random cutouts introduced by Mandelbrot in 1972. We then show how very precise information about the zero sets of CBI can be obtained in terms of the branching and immigrating mechanism