Quasi-stationary Distributions For Birth And Death Processes With Killing

For birth and death processes with killing(X(t),t?0)on the state space S={0,1,2....},where {1,2,...} is an irreducible class and 0 is an absorbing state which can be reached with certainty.The initial distribution v is called quasi-stationary distribution if the distribution of processes X(t)is not dependent on t before reached state 0,the main aims of this thesis are to study the quasi-stationary distributions and their domain of attraction problem for birth and death processes with killing.In the first chapter,we introduce the background and the research status of quasi-stationary distribution,then the main results of this thesis have been given.In the second chapter,the basic theory of Markov chains,the definitions of quasi-stationary distribution have been introduced,in the end,we calculate the decay parameter and construct all quasi-stationary distributions of random walk.In the third chapter,we study the quasi-stationary distribution for birth and death processes and domain of attraction of quasi-stationary distribution.For clearly ?-invariant measure,we give sufficient conditions to let v becoming quasi-stationary distribution,we also obtain a necessary and sufficient condition for ?_C-positive recurrence of the process,in the end,we give some sufficient conditions of domain of attraction at ?_C.