Leírás
Branching processes have been frequently used in biology, e.g., for modeling the spread of an infectious disease, for gene amplification and deamplification or for modeling telomere shortening, so their investigation is an essential topic. In this talk we will focus on describing the tail behavior of first- and second-order Galton--Watson processes with immigration in the presence of regularly varying distributions. Namely, we give sufficient conditions on the inital, offspring and immigration distributions under which a first- or second order Galton--Watson process with immigration is regularly varying. Moreover, in the second-order case we also give conditions under which the corresponding two-type Galton--Watson process with immigration has a unique stationary distribution such that its common marginals are regularly varying as well. Joint work with Mátyás Barczy and Gyula Pap.