Refracted Continuous-State Branching Processes: Self-regulating populations

TL;DR

This paper introduces a self-regulating continuous-state branching process that changes its growth rate based on population levels, using a Lamperti-like transform on refracted Lévy processes, with detailed mathematical properties.

Contribution

It presents a novel construction of refracted continuous-state branching processes with state-dependent growth parameters, expanding the modeling of self-regulating populations.

Findings

Derived the infinitesimal generator of the process

Analyzed probabilities of extinction and explosion

Established path properties of the process

Abstract

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