Poisson Representation of a Ewens Fragmentation Process
Poisson Representation of a Ewens Fragmentation Process
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埃文斯破碎过程的泊松表示
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Pitman
中科院分区：
文献类型：
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作者：
A. Gnedin;J. Pitman
本文给出了一个简单的显式构造，构造了一个在[n] = 1，. . .,θ ≥ 0时的n由带参数θ的Ewens抽样公式决定。随着n的变化，这些分区值过程是可交换的和一致的。它们可以通过从相应的质量碎裂过程中均匀采样得到，该过程是在泊松过程的点上切割一个单位间隔，强度为θx−1dx/mathbbR+，随着θ的增加而增强。
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of [n] = 1,. . .,n at time θ ≥ 0 is governed by the Ewens sampling formula with parameter θ. These partition-valued processes are exchangeable and consistent, as n varies. They can be derived by uniform sampling from a corresponding mass fragmentation process defined by cutting a unit interval at the points of a Poisson process with intensity θx−1dx on/mathbbR+, arranged to beintensifying as θ increases.