Entrance Laws for Continuous-State Nonlinear Branching Processes Coming Down from Infinity

We consider a class of non-negative valued, time-changed spectrally positive Lévy processes stopped whenever hitting 0, which can be identified as continuous-state branching processes with population dependent branching rates. Given the process comes down from infinity, we find expressions for Laplace transform of the first passage time and for the potential measure for the process started from infinity. Those expressions are in terms of the generalized scale functions for the corresponding spectrally positive Lévy processes.