NECESSARY AND SUFFICIENT CONDITIONS FOR REALIZABILITY OF POINT PROCESSES
NECESSARY AND SUFFICIENT CONDITIONS FOR REALIZABILITY OF POINT PROCESSES
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DOI：
10.1214/10-aap703
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发表时间：
2011-08-01
影响因子：
1.8
通讯作者：
Speer, Eugene R.
中科院分区：
文献类型：
--
作者：
Kuna, Tobias;Lebowitz, Joel L.;Speer, Eugene R.
本文给出了一对（广义）函数rho（1）（r（1））和rho（2）（r（1），r（2）），r（i）是X中的一个元素，是拓扑空间X中某个点过程，例如R（d），Z（d）或它们的子集的稠密性和对相关性的充要条件.这是经典的“截断矩”问题的无限维版本。标准技术适用于X的任何紧致子集中只能有有限个点的情况。没有这个限制，我们得到，对于紧X，加强的条件是必要的和充分的过程满足进一步的要求-存在一个有限的三阶矩的存在。当X不是紧的时，我们以两种不同的方式推广后面的条件。
We give necessary and sufficient conditions for a pair of (generalized) functions rho(1)(r(1)) and rho(2) (r(1), r(2)), r(i) is an element of X, to be the density and pair correlations of some point process in a topological space X, for example, R(d), Z(d) or a subset of these. This is an infinite-dimensional version of the classical "truncated moment" problem. Standard techniques apply in the case in which there can be only a bounded number of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further requirement-the existence of a finite third order moment. We generalize the latter conditions in two distinct ways when X is not compact.