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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.
Advances in Applied Probability
|September 26, 2025
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.
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.
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