论文标题
雷骑士的雷克代表
A Ray-Knight representation of up-down Chinese restaurants
论文作者
论文摘要
我们研究了在中国餐厅流程（CRP）框架中自然出现的构图价值连续时间马尔可夫连锁店。随着时间的流逝，新客户到达（上步），现有客户以源自Pitman and Winkel（2009）的CRP的合适价格离开（下步）。我们将这种上下的CRP与兰伯特（2010）诱导频谱积极过程的分裂树相关联。相反，我们开发了Ray-knight类型的定理，以从Lévy过程的高度恢复更通用的上下CRP，并以整数价值路径标记的跳跃。我们进一步建立了Lévy过程的限制定理，以及由Forman等人连接到工作的整数值的途径。 （2018+）在间隔分区的扩散及其一些长期的猜想中。
We study composition-valued continuous-time Markov chains that appear naturally in the framework of Chinese Restaurant Processes (CRPs). As time evolves, new customers arrive (up-step) and existing customers leave (down-step) at suitable rates derived from the ordered CRP of Pitman and Winkel (2009). We relate such up-down CRPs to the splitting trees of Lambert (2010) inducing spectrally positive Lévy processes. Conversely, we develop theorems of Ray-Knight type to recover more general up-down CRPs from the heights of Lévy processes with jumps marked by integer-valued paths. We further establish limit theorems for the Lévy process and the integer-valued paths to connect to work by Forman et al. (2018+) on interval partition diffusions and hence to some long-standing conjectures.
