Multitype Branching Processes in Random Environment: Probability of Survival for the Critical Case
2018
We investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in an environment generated by a sequence of independent identically distributed random variables. Under fairly general assumptions on the form of the offspring generating functions of particles, we show that the probability of survival up to generation $n$ of the process initiated at moment zero by a single particle of type $i$ is equivalent to $\beta_in^{-1/2}$, where $\beta_i$ is a positive constant. This assertion essentially generalizes a number of previously known results.
Keywords:
- Generating function
- Branching (version control)
- Asymptotic analysis
- Assertion
- Mathematical analysis
- Branching process
- Mathematics
- Independent and identically distributed random variables
- Beta (finance)
- Random variable
- random environment
- Statistical physics
- change of measure
- survival probability
- Statistics
- probability of survival
- Correction
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- Cite
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