Lamperti transformation for continuous-state branching processes with competition and applications

The Lamperti transformation is established between continuous-state branching processes (CB-processes) with competition and strong solutions of a certain type of stochastic equations driven by Lévy processes without negative jumps. Using this result we study the maximal jumps of CB-processes with competition. In particular, we obtain the distributions of the maximal jumps of CB-processes and logistic branching processes.