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MULTITYPE BRANCHING PROCESSES WITH INHOMOGENEOUS POISSON IMMIGRATION.

Kosto V Mitov1, Nikolay M Yanev2, Ollivier Hyrien3

  • 1Faculty of Aviation, Vasil Levski National Military University, 5856 D. Mitropolia, Pleven, Bulgaria.

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PubMed
Summary

This study introduces multitype branching processes with inhomogeneous Poisson immigration. Researchers analyzed the critical Markov case, revealing limit distributions and asymptotic behaviors based on changing intensity functions.

Keywords:
60J8562P10Multitype branching processPrimary 60J80Secondary 60F05immigrationinhomogeneous Poisson processlimit distribution

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Area of Science:

  • Stochastic processes
  • Probability theory
  • Mathematical biology

Background:

  • Branching processes are fundamental models in probability and population dynamics.
  • Inhomogeneous Poisson immigration adds complexity to standard branching models.
  • Understanding critical cases is crucial for predicting population behavior.

Purpose of the Study:

  • To introduce and analyze multitype branching processes with inhomogeneous Poisson immigration.
  • To investigate the critical Markov case where intensity is a regularly varying function.
  • To determine limit distributions and asymptotic behaviors.

Main Methods:

  • Development of multitype branching process theory.
  • Analysis of critical Markov cases with regularly varying intensity functions.
  • Asymptotic analysis of moments and nonextinction probabilities.

Main Results:

  • Derivation of various conditional and unconditional multitype limit distributions.
  • Identification of dependencies between distributions and the rate of change in intensity.
  • Characterization of asymptotic behavior for moments and nonextinction probability.

Conclusions:

  • The behavior of these complex branching processes is significantly influenced by the dynamics of the immigration intensity.
  • The study provides a comprehensive framework for analyzing critical multitype branching processes.
  • Results have implications for modeling evolving populations in stochastic environments.