Some limit theorems for the critical Galton–Watson branching processes - Kudratov, Kh.; Khusanbaev, Ya. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 519.21 We consider critical Galton–Watson processes starting from a random number of particles and determine the effect of the mean value of the initial state on the asymptotic state of the process. For processes starting from a large number of particles and satisfying the condition (S), we prove the limit theorem similar to the result of W. Feller. We also prove the theorem under the condition W(n)>0 for critical processes satisfying the conditions (S) and (M).