A1521
Title: Markov branching processes with infinite mean immigration
Authors: Penka Mayster - Institute of Mathematics and Informatics-Bulgarian Academy of Sciences (Bulgaria)
Maroussia Slavtchova-Bojkova - Sofia University (Bulgaria) [presenting]
Abstract: Continuous-time branching processes with immigration were first introduced by B. A. Sevastyanov. In these models, immigration occurs according to a homogeneous Poisson process. Specifically, at the jump points of the Poisson process, a random number of new individuals (or particles) arrive, which then reproduce independently according to a continuous-time Markov branching process (CTMBP). The goal is to study the impact of immigration characterized by infinite mean and variance, driven by a discrete-stable compound Poisson process within the framework of CTMBP. In particular, the aim is to derive the explicit form of the probability-generating function for these processes, as well as the probability of extinction. Ultimately, the limiting behavior of such processes is analyzed.
