Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617929 | Journal of Mathematical Analysis and Applications | 2012 | 6 Pages |
Abstract
We obtain a sufficient condition for an initial distribution to be in the domain of attraction of the quasi-stationary distribution for a linear birth and death process by two methods, that is, let M={mi,i=1,2,…} be a probability distribution with ∑iimi<∞∑iimi<∞, thenlimt→∞PM(X(t)=j|T>t)=νj, where νjνj is a geometric distribution with parameter λ/μλ/μ. The first method acquires the results by computing directly while the second method bases on the theory of probability generating function.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hanjun Zhang, Wenbo Liu,