TY - JOUR
AU - Kh. Kudratov
AU - Ya. Khusanbaev
PY - 2023/05/10
Y2 - 2024/07/20
TI - Some limit theorems for the critical Galton–Watson branching processes
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 75
IS - 4
SE - Research articles
DO - 10.37863/umzh.v75i4.6781
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6781
AB - UDC 519.21We 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 $(M).$
ER -