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Limiting Distributions for Multitype Branching Processes
Andrei Y Yakovlev1, Nikolay M Yanev
1University of Rochester and Institute of Mathematics, Sofia.
Stochastic Analysis and Applications
|September 14, 2013
Summary
This study analyzes multitype Markov branching processes, proving multivariate asymptotic normality for both process behavior and relative frequencies. These findings are crucial for cell kinetics research.
Area of Science:
- Probability Theory
- Stochastic Processes
- Mathematical Biology
Background:
- Markov branching processes are fundamental models in probability.
- Understanding asymptotic behavior is key for long-term predictions.
- Previous work focused on fixed time, limiting the scope for dynamic systems.
Purpose of the Study:
- Investigate the asymptotic behavior of multitype Markov branching processes.
- Obtain limiting distributions and prove multivariate asymptotic normality.
- Analyze relative frequencies of distinct types for biological applications.
Main Methods:
- Asymptotic analysis of Markov branching processes.
- Techniques for discrete and continuous time models.
- Mathematical derivations for limiting distributions and normality.
Main Results:
- Established asymptotic behavior for large initial ancestors and infinite time.
- Proved multivariate asymptotic normality for the processes.
- Derived non-random limits for relative frequencies, showing asymptotic normality.
Conclusions:
- The study provides new limiting results for Markov branching processes.
- Findings are particularly relevant for cell kinetics where relative frequencies are measurable.
- Extends previous research by considering infinite time horizons.
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