论文标题
带有泊松 - 二硫酸盐固定分布的测量值扩散的两参数家族
A two-parameter family of measure-valued diffusions with Poisson-Dirichlet stationary distributions
论文作者
论文摘要
我们提供了纯原子 - 含量值的扩散的两参数家族的路线构造，其中poisson-dirichlet $（α，θ）$分布的排名是固定的，以$α\ in（0,1）$和$θ\ ge 0 $ 0 $。这解决了冯和太阳（2010）的猜想。我们以$（α，0）$ - 和$（α，α）$ - 间隔分区的发展为基础。的确，我们首先从稳定过程的水平中提取自相似的超级过程，这些过程的跳跃装饰有平方的贝塞尔游览和不同的等位基因类型。我们通过改变时间和对单位质量的归一化来完成构造。在一份同伴论文中，我们表明，根据Petrov（2009）引入的两参数扩散家族，该量值值的过程的排名进化，扩大了Ethier和Kurtz（1981）的工作。这些排名的质量扩散是在中国餐厅流程上上下马尔可夫连锁店的连续限制。
We give a pathwise construction of a two-parameter family of purely-atomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson-Dirichlet$(α,θ)$ distributions, for $α\in (0,1)$ and $θ\ge 0$. This resolves a conjecture of Feng and Sun (2010). We build on our previous work on $(α,0)$- and $(α,α)$-interval partition evolutions. Indeed, we first extract a self-similar superprocess from the levels of stable processes whose jumps are decorated with squared Bessel excursions and distinct allelic types. We complete our construction by time-change and normalisation to unit mass. In a companion paper, we show that the ranked masses of the measure-valued processes evolve according to a two-parameter family of diffusions introduced by Petrov (2009), extending work of Ethier and Kurtz (1981). These ranked-mass diffusions arise as continuum limits of up-down Markov chains on Chinese restaurant processes.
