The Quasi-stationary Distribution And Their Domain Of Attraction Problem Of The Linear Birth And Death Press

This master thesis starts a Birth and Death Process model , Q - matrixbe defined as ,λi = iλ,μi = iμwhen i∈N ,λ,μindicate birth rate anddeath rate . By summarizing the random model system and Q-matrix propertiesdiscussing , stochastic process draw some conclusions such as ergodic recurrencestationary distributions, limit distributions , quasi- limit distributions and so onthe stochastic process of basic fundamental theorem. This is first part of thesis .The second part is that I consult some famous people'conclusions. dis-cussing the quasi- stationary distribution's domain of attraction. the inspirationcome from a famous author Van Doorn write a paper named quasi- stationarydistribution and quasi- stationary distribution convergence , he wrote that from asingle set, quasi-limiting distribution converge a geometric distribution, I gain en-lightenment from Mr.zhang ,if given some particular conditions, beginning froma distribution then still converge a geometric distribution. In the birth and deathprocess quasi- stationary distribution is geometric distribution .I turn out thaton the condition imi <∞,which mi = 1 is a probability distribution. ThenI give a simple way to countξ1 ,ξ1 is Q matrix's the second characteristic valueand the first characteristic value margin.