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On asymptotic normality of the total progeny in the positive recurrent Q-processes
Azam A. Imomov, Zuhriddin A. Nazarov
We examine the population growth system called Q-processes. This is defined by the Galton-Watson Branching system conditioned on non-extinction of its trajectory in the remote futu…
Further remarks on the explicit generating function expression of the invariant measure of critical Galton-Watson Branching Systems
Azam A. Imomov
Consider the critical Galton-Watson branching system with infinite variance of the offspring law. We provide an alternative arguments against what Slack~{\cite{Slack68}} did when i…
Some remarks on the direct calculation of Probabilities in Urn Schemes
Azam A. Imomov, Yorqin Khodjaev
The paper considers urn schemes in which several urns can be involved. Simplified formulas are proposed that allow direct calculation of probabilities without the use of elements c…
On asymptotic structure of the critical Galton-Watson Branching Processes with infinite variance and Immigration
Azam A. Imomov, Erkin E. Tukhtaev
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.