2023/06/14 by Азам А. Имомов, Imomov, Azam A., Zuhriddin A. Nazarov +1
Mathematics · Business, Management and Accounting · #Stochastic processes and statistical mechanics #Advanced Queuing Theory Analysis #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2306.09367
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 future. In this paper we observe the total progeny up to time n in the Q-process. By analogy with branching systems, this variable is of great interest in studying the deep properties of the Q-process. We find that the sum total progeny as a random variable approximates the standard normal distribution function under a second moment assumption for the initial Galton-Watson system offspring law. We estimate the speed rate of this approximation.