Renewed limit theorems for the discrete-time Branching Process and its conditioned limiting law interpretation
Journal: NEW TRENDS IN MATHEMATICAL SCIENCES (Vol.4, No. 4)Publication Date: 2016-09-01
Authors : Azam Imomov;
Page : 213-238
Keywords : Branching process transition function Q-process invariant measures ergodic chain total states joint distribution limit theorem.;
Abstract
Our principal aim is to observe a 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 state and prove the analogue of Law of large numbers and the Central limit theorem for total state of Q-process.
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