论文标题
二次马尔可夫分支过程的Sturm-Liouville理论和衰减参数
Sturm-Liouville Theory and Decay Parameter for Quadratic Markov Branching Processes
论文作者
论文摘要
对于二次马尔可夫分支过程（QMBP），我们表明衰减参数等于与PDE相关的Sturm-liouville操作员的第一个特征值，即过渡概率的生成函数满足。证明基于Sturm-Liouville操作员的光谱特性。衰减参数的上限和下限均通过强大的不平等版本明确给出。提供了两个示例来说明我们的结果。重要的数量是与QMBP的衰减参数紧密相关的Hardy指数，并进行了深入研究和估计。
For a quadratic Markov branching process (QMBP), we show that the decay parameter is equal to the first eigenvalue of a Sturm-Liouville operator associated with the PDE that the generating function of the transition probability satisfies. The proof is based on the spectral properties of the Sturm-Liouville operator. Both the upper and lower bounds of the decay parameter are given explicitly by means of a version of Hardy inequality. Two examples are provided to illustrate our results. The important quantity, the Hardy index, which is closely linked with the decay parameter of QMBP, is deeply investigated and estimated.
