树上生灭过程的Dirichlet特征值估计

Estimation of the Dirichlet Eigenvalue of Birth-Death Process on Trees

本文给出树上两类非常返的生灭过程的第一Dirichlet特征值的变分公式．一类是配称测度有限时,给出以根为吸收点的Dirichlet特征值的变分公式;另一类是配称测度无限时,给出树上生灭过程的Dirichlet主特征值的变分公式．

In this paper, we give out variational formula for the first Dirichlet eigenvalues of two kinds of transient birth-Death processes on trees. One is that the symmetric measure of the process is finite but the root of the tree is switched to an absorbing state; another is that the symmetric measure is infinite.