论文标题
马尔可夫分支过程的条件限制结构，没有有限的第二刻
On conditioned limit structure of the Markov branching process without finite second moment
论文作者
论文摘要
考虑连续的马尔可夫分支过程。在关键情况下，我们考虑了一种情况，当颗粒变化强度具有无限第二时的生成函数，但其尾巴经常在karamata意义上有所不同。首先，我们讨论该过程过渡功能的限制属性。我们证明了局部限制定理并研究了该过程的千古特性。此外，我们调查了限制概率函数的条件永远不会灭绝。因此，我们获得了一个新的随机人口过程，作为一个连续的马尔可夫链，称为Markov Q-Process。我们研究马尔可夫Q过程的主要特性。
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense of Karamata. First we discuss limit properties of transition functions of the process. We prove local limit theorems and investigate ergodic properties of the process. Further we investigate limiting probability function conditioned to be never extinct. Hereupon we obtain a new stochastic population process as a continuous-time Markov chain called the Markov Q-Process. We study main properties of Markov Q-Process.
