Poisson process Fock space representation, chaos expansion and covariance inequalities
Poisson process Fock space representation, chaos expansion and covariance inequalities
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泊松过程福克空间表示、混沌展开和协方差不等式
DOI：
10.1007/s00440-010-0288-5
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发表时间：
2009
影响因子：
2
通讯作者：
M. Penrose
中科院分区：
文献类型：
--
作者：
G. Last;M. Penrose
考虑任意可测空间上具有任意有限强度测度的泊松过程η。建立了η的平方可积函数的显式Fock空间表示。作为结果，我们明确地确定，在迭代差分算子，在Wiener-Itô混沌展开的积分。我们应用这些结果将已知的齐次泊松过程的方差不等式推广到一般泊松情况。庞加莱不等式是一个特例。进一步的应用是（严格）有序空间上泊松过程的协方差恒等式和η单调函数的harris - fkg不等式。
We consider a Poisson process η on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of η. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener–Itô chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincaré inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris–FKG-inequalities for monotone functions of η.