The renewed limit theorems for the discrete-time branching process and its conditioned limiting law interpretation
Азам А. ИмомовState Testing Center, Under the Cabinet of Ministers of the Republic of Uzbekistan and Institute of Mathematics at the National University of Uzbekistan
ABI
Аннотация
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma. Afterwards we get a Differential analogue of the Basic Lemma. This Lemma plays main role in our discussions throughout the paper. Hereupon we improve and supplement classical results concerning Galton-Watson process. Further we investigate properties of the population process so called Q-process. In particular we obtain a joint limit law of Q-process and its total state. And also we prove the analogue of Law of large numbers and the Central limit theorem for total state of Q-process.
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