The Ergodicity In A Class Of Non-minimal Birth-death Processes

As an important Markov Process,the ergodicity and convergence rate of birth and death process are hot spots about Markov Chains.Previous studies are essentially the assumption that Q matrix is regular,that is a minimal birth-death process.This paper researches the ergodicity in a class of non-minimal birth and death process by breaking the conditions of minimal process.The research in this paper is about the ergodicity of the birth and death process with∞which is outflow case.First of all,this paper proves ergodicity and obtains the transition function of the expression of the stationary distribution;Then this paper prooves this type of birth and death process with strong ergodicity;At last this paper calculates E^∞{e^λσo} in excursion space and gets the exponential ergodicity of transition function and the largest index of ergodicity ergodic constant estimated.The research shows that the stationary distribution and ergodic speed of birth-death process depend on the structure.