The Decay Parameter And The Quasi-stationary Distribution Of The Generalized Branching Processes

This thesis primarily studies the related properties of the subcritical branch-ing processes and the collision branching processes.For a start,some conclusions of the subcritical branching processes are obtained by using a new method,in-cluding the decay parameter?_Cof the subcritical branching processes,the?_C-invariant measure and the specific expression of the processes's generating func-tion of the quasi-stationary distribution,as well as the domain of attraction of the subcritical branching processes.Subsequently,the collision branching processes are studied by this method,a lower bound of the decay parameter of the collision branching processes is given.Eventually,the concrete expression of the generating function of the quasi-stationary distribution is obtained.