On the hitting times of continuous-state branching processes with immigration

We study the two-dimensional joint distribution of the first hitting time of a con-stant level by a continuous-state branching process with immigration and their primitive stopped at this time. We show an explicit expression of its Laplace transform. Using this formula, we study the polarity of zero and provide a necessary and sufficient criterion for transience or recurrence. We follow the approach of Shiga, T. (1990) [A recurrence crite-rion for Markov processes of Ornstein-Uhlenbeck type. Probability Theory and Related Fields, 85(4), 425-447], by finding some λ-invariant functions for the generator. Key words. Continuous-state branching processes, immigration, first hitting time, transience and recurrence, polarity. Mathematics Subject classification (2010): 60J80 60J25 60G1