论文标题
固定连续状态分支过程的某些特性
Some properties of stationary continuous state branching processes
论文作者
论文摘要
我们考虑了随着移民的静止连续分支过程的家谱树。对于亚临界稳定的分支机制，我们在某个固定时间考虑了现有种群的家谱树，并证明，直到确定性的时间变化，它被分布成连续的时代Galton-Watson工艺，随着移民的移民。当仅查看到达某些固定时间间隔的移民时，我们获得了关键的稳定分支机制的相似结果。对于一种一般的亚临界分支机制，我们考虑了给出现存人群中后代的个体的数量。相关的过程（时间向前或向后）是纯粹的死亡或纯马尔可夫过程，为此我们计算过渡速率。
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove that, up to a deterministic time-change, it is distributed as a continuous-time Galton-Watson process with immigration. We obtain similar results for a critical stable branching mechanism when only looking at immigrants arriving in some fixed time-interval. For a general sub-critical branching mechanism, we consider the number of individuals that give descendants in the extant population. The associated processes (forward or backward in time) are pure-death or pure-birth Markov processes, for which we compute the transition rates.
