Sufficient conditions are given for CIMBI processes to avoid the boundary entirely and for hitting it almost surely (diffusion case) or with positive probability (finite-activity jumps) under small constant immigration.
Explosion of continuous-state branching processes with competition in a Lévy environment
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Boundary behavior of continuous-state interacting multi-type branching processes with immigration
Sufficient conditions are given for CIMBI processes to avoid the boundary entirely and for hitting it almost surely (diffusion case) or with positive probability (finite-activity jumps) under small constant immigration.