Some limit theorems for the critical Galton–Watson branching processes

  • Kh. Kudratov National University of Uzbekistan, Tashkent
  • Ya. Khusanbaev Institute of Mathematics, Tashkent, Uzbekistan
Keywords: Critical Galton-Watson process, generating function, slowly varying function.


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 $(M).$


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How to Cite
Kudratov, K., and Y. Khusanbaev. “Some Limit Theorems for the Critical Galton–Watson Branching Processes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 4, May 2023, pp. 467 -7, doi:10.37863/umzh.v75i4.6781.
Research articles