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We construct a modified continuous-state branching process whose Malthusianparameter is replaced by another when passing below a certain level. Theconstruction is obtained via a Lamperti-like transform applied to a refractedL\'evy process. Infinitesimal generator, probability of vanishing at infinity,of explosion and some path properties are also provided.

Refracted Continuous-State Branching Processes: Self-regulating populations