论文标题
亚临界马尔可夫分支过程中的扩展Sibuya分布
Extended Sibuya distribution in the Subcritical Markov Branching processes
论文作者
论文摘要
亚临界马尔可夫分支过程x（t）从一个粒子开始，因为初始条件具有最终的灭绝概率q = 1。考虑的分支机理由非负整数上的对数分布的混合物定义。本文的目的是证明，在这种情况下，粒子的随机数x（t）在时间t> 0遵循移动的扩展Sibuya分布，其参数取决于时间$ t> 0 $。条件上限的概率正是正整数支持的对数序列分布。
The subcritical Markov branching process X(t) starting with one particle as the initial condition has the ultimate extinction probability q = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions on the nonnegative integers. The purpose of the present paper is to prove that in this case the random number of particles X(t) alive at time t>0 follows the shifted extended Sibuya distribution, with parameters depending on the time $t>0$. The conditional limit probability is exactly the logarithmic series distribution supported by the positive integers.
