TY - JOUR AU - Lysetskyi, T. B. AU - Yeleiko, Ya. I. PY - 2021/10/22 Y2 - 2024/03/29 TI - LIMIT THEOREMS FOR TOTAL NUMBER OF PARTICLES IN CRITICAL AGE-DEPENDENT BRANCHING PROCESSES JF - PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number JA - Number VL - IS - 16(60) SE - Mathematics and Mechanics DO - 10.31471/2304-7399-2021-16(60)-33-46 UR - https://pvntsh.nung.edu.ua/index.php/number/article/view/1702 SP - 33-46 AB - <p><em>In this paper we considercritical multitype age-dependent branching processes. It is known, that in case with constant transition probabilities in processes with immigration total numbers of particles in process born by t, divided by t<sup>2</sup>tends in probability to infinitely divisiblelaw, whose Laplace transform is explicitly given and in processes without immigration similar convergence holds but under the condition of non-extinction of process by t. Here we prove given results in case with variable transition probabilities.</em></p> ER -