Abstract
The purpose of this article is to observe that the zero sets of continuous-state branching processes with immigration (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.
Citation
Clément Foucart. Gerónimo Uribe Bravo. "Local extinction in continuous-state branching processes with immigration." Bernoulli 20 (4) 1819 - 1844, November 2014. https://doi.org/10.3150/13-BEJ543
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