@article{Kudratov_Khusanbaev_2023, title={Some limit theorems for the critical Galton–Watson branching processes}, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6781}, DOI={10.37863/umzh.v75i4.6781}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>UDC 519.21</p> </div> </div> </div> <p>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.<span class="Apple-converted-space">&nbsp;</span>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.&nbsp;We also prove the theorem under the condition $W(n)&gt;0$ for critical processes satisfying the conditions $(S)$&nbsp;and $(M).$</p&gt;}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Kudratov, Kh. and Khusanbaev, Ya.}, year={2023}, month={May}, pages={467 - 477} }