We study by duality methods the extinction and explosion times of continuous-state branching processes with logistic competition (LCSBPs) and identify the local time at \(\infty \) of the process when its boundary \(\infty \) is regular reflecting. The main idea is to introduce a certain “bidual” process V of the LCSBP Z. The latter is the Siegmund dual process of the process U, that was introduced in Foucart (2019) as the Laplace dual of Z. By using both dualities, we shall relate local explosions and the extinction of Z to local extinctions and the explosion of the process V. The process V being a one-dimensional diffusion on \([0,\infty ]\) , many results on diffusions can be used and transferred to Z. A concise study of Siegmund duality for one-dimensional diffusions and their boundaries is also provided.
