论文标题
更新的限制了离散时间分支过程及其条件限制法律解释的定理
Renewed Limit Theorems for the discrete-time Branching Process and its Conditioned Limiting Law interpretation
论文作者
论文摘要
我们的主要目的是观察马尔可夫离散时间的人口增长过程，并具有长期的轨迹。首先，我们研究Galton-Watson过程的渐近衰减，以作为基本的引理。之后，我们得到了基本引理的不同类似物。这种引理在整本论文的讨论中扮演着主要的角色。因此，我们改进和补充有关Galton-Watson流程的经典结果。此外，我们研究了所谓的Q过程的人口过程的特性。特别是，我们获得了Q-Process及其总州的联合限制定律。而且，我们还证明了大量法律的类似物和Q-Process总状态的中心限制定理。 关键字：分支过程；过渡功能； Q-PROCESS;不变措施；沿阵行链；总州；联合分布；限制定理。
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma. Afterwards we get a Differential analogue of the Basic Lemma. This Lemma plays main role in our discussions throughout the paper. Hereupon we improve and supplement classical results concerning Galton-Watson process. Further we investigate properties of the population process so called Q-process. In particular we obtain a joint limit law of Q-process and its total state. And also we prove the analogue of Law of large numbers and the Central limit theorem for total state of Q-process. Keywords: Branching process; transition function; Q-process; invariant measures; ergodic chain; total states; joint distribution; limit theorem.
