h-变换在生灭过程中的应用

Applications of h-transformation for Birth-death Processes

考虑Z+∶={0,1,2,…}上0与∞均为Dirichlet边界暂留生灭过程的第一特征值λ0.通过适当的h-变换,结合0为Dirichlet边界常返生灭过程的第一特征值现有结果,得到λ0的精细估计,并利用h-变换给出上述特征值λ0对应Poincaré型不等式最优常数的估计.

Consider the first eigenvalue λ0 of transient birth-death processes on Z＋：= 0,1,2,with Dirichlet boundary at O and ∞. By adopting the proper h-transformation and making full use of existing results for ergodic birth-death processes with Dirichlet boundary at O, obtain explicit estimates for λ0 - Furthermore, the h-transformation applies to study the associated Poincare-type inequalities.