The Quasi-stationary Distribution And Their Domain Of Attraction Problem

In this paper,we mainly study the quasi-stationary distributions and theirdomain of attraction problem,especially in the birth and death process.In the first chapter,we introduce the background,history,current situationand basic theory of quasi-stationary distributions.In the second chapter,the quasi-stationary distributions for a linear birthand death process is determined by two methods. The first method obtains ourdesired results by computing directly while the second method bases on the re-lationship between quasi-stationary distributions and its limiting of probabilitygenerating function. In addition,we also obtain the stationary distribution for alinear birth,death and immigration process with the second method.In the third chapter,we obtain the domain of attraction of the quasi-stationarydistribution for a linear birth and death process by the similar methods with lastchapter.In the fourth chapter,we derive the domain of attraction of the quasi-stationarydistributions for a birth and death process ,which generalize the above results .Ourmain tool will be Karlin and McGregor's spectral representation for the transitionprobabilities of a birth and death process ,orthogonal polynomial and a dualityconcepts for birth and death processes.