标题： 关于可交换协聚过程的块计数过程和固定线 显示英文标题

标题： On the block counting process and the fixation line of exchangeable coalescents

摘要： 我们研究可交换的共轭过程的块计数过程和固定线。 提供了这两个过程的无穷小速率的公式。 证明了块计数过程是固定线的Siegmund对偶。 对于限制在大小为n的样本上且有尘埃的可交换共轭过程，当n趋于无穷时，提供了块计数过程的收敛结果。 相关的极限过程与共轭过程的单例频率有关。 通过对偶性，我们得到了具有尘埃的可交换共轭过程的固定线的类似收敛结果。 详细研究了Dirichlet共轭过程和Poisson-Dirichlet共轭过程。 显示英文摘要

摘要： We study the block counting process and the fixation line of exchangeable coalescents. Formulas for the infinitesimal rates of both processes are provided. It is shown that the block counting process is Siegmund dual to the fixation line. For exchangeable coalescents restricted to a sample of size n and with dust we provide a convergence result for the block counting process as n tends to infinity. The associated limiting process is related to the frequencies of singletons of the coalescent. Via duality we obtain an analog convergence result for the fixation line of exchangeable coalescents with dust. The Dirichlet coalescent and the Poisson-Dirichlet coalescent are studied in detail.