论文标题
在Galton-Watson分支过程中，Kolmogorov常数的明确形式
On explicit form of the Kolmogorov constant in the theory of Galton-Watson Branching Processes
论文作者
论文摘要
该论文认为众所周知的加尔顿·沃森随机分支过程。我们正在处理一个非关键案件。在亚临界情况下，当每个粒子的直接后代的平均值平均值小于1时，在过程的正轨迹上，粒子数量的人数平均值稳定并接近1/K，其中k是所谓的kolmogorov常数。该论文专用于搜索该常数的明确表达，这取决于该过程的结构参数。我们的推理本质上是基于基本的引理，该引理描述了颗粒数量分布的生成功能的渐近扩展。所谓的Q-Process的过渡概率及其特性收敛到不变度的措施的过渡概率的渐近性能也起着重要的作用。
The paper considers the well-known Galton-Watson stochastic branching process. We are dealing with a non-critical case. In the subcritical case, when the mean of the direct descendants of one particle per generation of the time step is less than 1, the population mean of the number of particles on the positive trajectories of the process stabilizes and approaches 1/K, where K is the so-called Kolmogorov constant. The paper is devoted to the search for an explicit expression of this constant depending on the structural parameters of the process. Our reasoning is essentially based on the Basic Lemma, which describes the asymptotic expansion of the generating function of the distribution of the number of particles. An important role is also played by the asymptotic properties of the transition probabilities of the so-called Q-process and their property convergence to invariant measures.
