The Height Process of a Continuous-State Branching Process with Interaction

Zenghu Li (), Etienne Pardoux () and Anton Wakolbinger ()
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Zenghu Li: Beijing Normal University
Etienne Pardoux: Aix Marseille Univ
Anton Wakolbinger: Goethe-University

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 142-185

Abstract: Abstract For a generalized continuous-state branching process with non-vanishing diffusion part, finite expectation and a directed (“left-to-right”) interaction, we construct the height process of its forest of genealogical trees. The connection between this height process and the population size process is given by an extension of the second Ray–Knight theorem. This paper generalizes earlier work of the two last authors which was restricted to the case of continuous branching mechanisms. Our approach is different from that of Berestycki et al. (Probab Theory Relat Fields 172:725–788, 2018). There the diffusion part of the population process was allowed to vanish, but the class of interactions was more restricted.

Keywords: Continuous-state branching process; Population dynamics with interaction; Genealogy; Height process of a random tree; Primary 60J80; 60J25; 60H10; Secondary 92D25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01054-5

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