Birth-death processes on trees

作者：Ma YuTao^*

来源：Science China Mathematics, 2010, 53(11): 2993-3004.

DOI：10.1007/s11425-010-4077-5

• birth-death process
• tree
• ergodicity
• Dirichlet eigenvalue

In this paper, we consider birth-death processes on a tree T and we are interested when it is regular, recurrent and ergodic (strongly, exponentially). By constructing two corresponding birth death processes on Z(+), we obtain computable conditions sufficient or necessary for that (in many cases, these two conditions coincide). With the help of these constructions, we give explicit upper and lower bounds for the Dirichlet eigenvalue lambda(0). At last, some examples are investigated to justify our results.

• 出版日期2010-11
• 单位北京师范大学