Author: Hart, Andrew; Modeling, Servet Mart'inez Center for Mathematical; CNRS-UCHILE, UMI 2071; Matem'aticas, Facultad de Ciencias F'isicas y; Chile, Universidad de; Santiago,; Chile,
Title: Finite delayed branching processes Cord-id: i6za8uq9 Document date: 2021_1_17
ID: i6za8uq9
Snippet: We describe and study the delayed multi-type branching process, a finite-time delayed multi-type branching process in which individuals are active (can reproduce offspring) during a finite time interval of random length bounded by~$D$. We show that the criterion for extinction is similar to that for the non-delayed case but is based on the sum of the mean matrices rather than a single mean matrix. In the supercritical case we impose the condition that the mean matrices at each delay offset share
Document: We describe and study the delayed multi-type branching process, a finite-time delayed multi-type branching process in which individuals are active (can reproduce offspring) during a finite time interval of random length bounded by~$D$. We show that the criterion for extinction is similar to that for the non-delayed case but is based on the sum of the mean matrices rather than a single mean matrix. In the supercritical case we impose the condition that the mean matrices at each delay offset share the right and left Perron-Frobenius eigenvectors. In this case we are able to give explicit analytic expressions for various quantities derived from the limit of the geometrically weighted mean evolution of the process.
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