Critical Markov branching processes with general set of types

Source abstract

This paper is concerned with the asymptotic behaviour of critical, quasi-positively regular Markov branching processes. Several results which have been established with restrictions on the set of types or on the parameter are proven on slightly different moment assumptions for an arbitrary set of types and continuous as well as discrete parameter. The methods employed are analytic and rest upon the properties of probability-generating functionals constructed from the given transition function.