Local extinction in continuous-state branching processes with immigration

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.

Published in at http://dx.doi.org/10.3150/13-BEJ543 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (5)

• On the Lamperti stable processes
• On the Eve property for CSBP
• Continuous-state branching processes
• Changing the branching mechanism of a continuous state branching process using immigration
• Time to MRCA for stationary CBI-processes

Cited by in corpus (7)

• Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes
• Existence of densities for multi-type CBI processes
• On the anisotropic stable JCIR process
• Boundary behavior of multi-type continuous-state branching processes with immigration
• Time to MRCA for stationary CBI-processes
• Totally Ordered Measured Trees and Splitting Trees with Infinite Variation II: Prolific Skeleton Decomposition
• A population model with non-neutral mutations using branching processes with immigration