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Local explosions and extinction of continuous state branching processes with logistic competition

Abstract : We study by duality methods the extinction and explosion times of continuousstate branching processes with logistic competition (LCSBPs) and identify the local time at ∞ of the process when it is instantaneously reflected at ∞. 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 [Fou19] 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, ∞], many results on diffusions can be used and transfered to Z. A concise study of Siegmund duality for regular one-dimensional diffusions is also provided.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03425834
Contributor : Clément Foucart Connect in order to contact the contributor
Submitted on : Thursday, November 11, 2021 - 2:41:42 PM
Last modification on : Sunday, November 28, 2021 - 3:29:11 AM
Long-term archiving on: : Saturday, February 12, 2022 - 6:15:56 PM

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  • HAL Id : hal-03425834, version 1

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Clément Foucart. Local explosions and extinction of continuous state branching processes with logistic competition. 2021. ⟨hal-03425834⟩

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