Estimation For Decay Parameter Of Markov Branching Processes

In this paper,we consider the power law processes which is the most representative Markov branching processes, calculating the decay parameter,discussing the existence of the quasi-stationary distribution by the way of birth-death processes,and the the relationship between the ergodicity and parameter v.The ?rst chapter,which is the introduction part,mainly introduces the research background and research status of branching processes and birth death processes.Including the basic concept and theory of continuous time Markov processes, and the quasi stationary distribution and decay parameters.In the second chapter, we do further researches in the decay properties and stochastic monotonicity of the power law branching processes on the basis of previous,investigate the existence and uniqueness of the quasi-stationary distribution.And we have a lower bound of the decay parameter through the numerical calculation method.The third chapter is based on the second chapter, we do a further promotion of the continuous time branching processes, and to study the decay properties,stochastic monotonicity and decay parameter’s properties.The fourth chapter gives a speci?c example, by using the method of numerical calculation,we get the decay parameter of a speci?c class power law processes.The ?fth chapter is a summary of the full text, and Prospect of this paper.