论文标题
两参数订购的中国餐厅流程的扩散极限
Diffusive limits of two-parameter ordered Chinese Restaurant Process up-down chains
论文作者
论文摘要
我们在$（0,1）$的一组开放子集上建造了一个两参数的Feller扩散家族，作为两参数订购的中餐厅进程的扩散极限。我们构造的扩散是彼得罗夫（Petrov）和库尔兹（Kurtz）无限无数的 - 中性 - 平行扩散模型的两参数扩展的自然有序类似物。最近，人们对构建的弥漫性散射的有序类似物产生了巨大的兴趣。现有的构建此类过程的方法是基于使用标记的Lévy过程的路径方法，并且对这些过程的出色猜想是，实际上，它们是我们在这里考虑的上订购的中国餐厅工艺的扩散限制。我们通过表明有订购的中国餐厅流程的扩散限制存在于此，我们在这一猜想上取得了进展。此外，我们的方法在用准对称函数的核心上产生了限制过程的生成器的简单，明确的描述。
We construct a two-parameter family of Feller diffusions on the set of open subsets of $(0,1)$ that arise as diffusive limits of two-parameter ordered Chinese Restaurant Process up-down chains. The diffusions we construct are natural ordered analogues of Petrov's two-parameter extension of Ethier and Kurtz's infinitely-many-neutral-alleles diffusion model. Recently, there has been significant interest in ordered analogues of the diffusions Petrov constructed. Existing methods for constructing such processes have been based on pathwise methods using marked Lévy processes and an outstanding conjecture about these processes is that they are, in fact, the diffusive limit of the ordered Chinese Restaurant Process up-down chains that we consider here. We make progress on this conjecture by showing that the diffusive limit of the ordered Chinese Restaurant Process up-down chains exists. Moreover, our methods yield a simple, explicit description of the generator of the limiting processes on a core described in terms of quasisymmetric functions.
