Critical Multitype Branching Processes with Random Migration
Miguel Gonz\'alez, Pedro Mart\'in-Ch\'avez, In\'es del Puerto
TL;DR
This paper introduces a critical multitype branching process with random migration, providing conditions for unbounded growth, analyzing asymptotic behavior, and deriving a diffusion approximation, extending classical branching process theory.
Contribution
It extends multitype branching processes by incorporating random migration and analyzes their critical behavior and asymptotics.
Findings
Conditions for unlimited growth or extinction.
Asymptotic distribution of the process.
Feller-type diffusion approximation.
Abstract
The aim of this paper is to introduce a multitype branching process with random migration following the research initiated with the Galton-Watson process with migration introduced in [Yanev & Mitov (1980) C. R. Acad. Bulg. Sci. 33(4):473-475]. We focus our attention in what we call the critical case. Sufficient conditions are provided for the process to have unlimited growth or not. Furthermore, using suitable normalizing sequences, we study the asymptotic distribution of the process. Finally, we obtain a Feller-type diffusion approximation.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics