On the central limit theorem for the stationary Poisson process of compact sets
On the central limit theorem for the stationary Poisson process of compact sets
复制标题
关于紧集平稳泊松过程的中心极限定理
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
V. Beneš
中科院分区：
文献类型：
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作者：
Z. Pawlas;V. Beneš
研究基于欧氏空间紧子集的平稳Poisson点过程的随机几何模型。利用Hausdorff测度和投影测度研究了ℝd上的随机测度。中心极限定理的表述方式使得能够比较所产生的随机测量强度的各种估计值。构造了强度的近似置信度区间。它们的用法在分段过程的长度强度估计的例子中得到了演示。(2014Wiley-VCH Verlag GmbH&Co.KGaA，Weinheim)
Stochastic geometry models based on a stationary Poisson point process of compact subsets of the Euclidean space are examined. Random measures on ℝd, derived from these processes using Hausdorff and projection measures are studied. The central limit theorem is formulated in a way which enables comparison of the various estimators of the intensity of the produced random measures. Approximate confidence intervals for the intensity are constructed. Their use is demonstrated in an example of length intensity estimation for the segment processes. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)