TY - JOUR
AU - Mayster, Penka
AU - Tchorbadjieff, Assen
PY - 2023/04/30
Y2 - 2023/06/09
TI - Extended Sibuya Distribution in Subcritical Markov Branching Processes
JF - Proceedings of the Bulgarian Academy of Sciences
JA - C. R. Acad. Bulg. Sci.
VL - 76
IS - 4
SE - Mathematics
DO - 10.7546/CRABS.2023.04.02
UR - https://proceedings.bas.bg/index.php/cr/article/view/285
SP - 517-524
AB - <p>The subcritical Markov branching process <em>X</em>(<em>t</em>) starting with one particle as the initial condition has the ultimate extinction probability <em>q</em> = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions on the nonnegative integers. The purpose of the present paper is to prove that in this case the random number of particles <em>X</em>(<em>t</em>) alive at time <em>t</em> > 0 follows the shifted extended Sibuya distribution, with parameters depending on the time <em>t</em> > 0. The conditional limit probability is the logarithmic series distribution supported by the positive integers. </p>
ER -