Research On The Existence Of Quasi-stationary Distribution Of Collision Branching Process

In this paper,we mainly study the collision branching process.Firstly,the domestic and foreign research progress of the collision branching process and the preliminary knowledge required in the paper are introduced.then,the -matrix of the process is introduced,and the process is extinct with probability 1 and the condition of limited average extinction time and specific expressions.the existence of the average extinction time limit of the process is proved by using two methods of the Lebesgue control convergence theorem and the monotonic convergence theorem,and the existence of the quasi-stationary distribution of the process is obtained.Finally,the relevant lemma is used to prove The attenuation parameter of the collision branching process is greater than 0,and the generating function of the decay parameter invariant distribution is obtained.