Study On The Quasi-stationary Distribution And Their Domain Of Atraction Problem Of A Class Of Birth And Death Processes

This paper based on the concrete model of a class of birth and death process(Q-matix be defined as bi=b,di=d,d? b.b,d indicate birth rate and death rate),this thesis focused on decay parameter ?C,transition probability function pij(t),quasi-stationary distributions(QSD)and their domain of attraction problem.Firstly,we gave a simple calculation method of decay parameters ?C.Sec-ondly,using the kolmogorov forward equation to solve the specific form of the transition probability function pij(t).Finally,we presented the quasi-stationary distribution of the model and analyzed their domain of attraction problem from a single set and a distribution.The inspiration comes from the article published by Van Doorn[20]in 1991:starting from a single set,quasi-limiting distribution converged a geometric distribution.In this model quasi-stationary distribution was geometric distribution,and related certification process was given.Further,we obtained a sufficient condition starting from a distribution which converged to quasi-stationary distribution.