胚粒模型空区危险函数的比较与渐近性
Comparisons and asymptotics for empty space hazard functions of germ-grain models
摘要：
本文研究了$\R^d$中稳态胚粒模型的空空间的随机性质，特别是讨论了关于一般结构元的空空间的内半径，该结构元允许是低维的.我们考虑泊松簇胚粒模型和布尔模型的颗粒是集群的凸体，并表明，更多的可变大小的集群的结果在随机更大的空空间的空空间的危险函数。我们还研究了集群在空间上的分布对空区风险值的影响。进一步得到了空空间危险函数在零点和无穷远处的渐近性质。
英文摘要：
We study stochastic properties of the empty space for stationary germ-grain models in $\R^d$, in particular we deal with the inner radius of the empty space with respect to a general structuring element which is allowed to be lower-dimensional. We consider Poisson cluster germ-grain models and Boolean models with grains that are clusters of convex bodies and show that more variable size of clusters results in stochastically greater empty space in terms of the empty space hazard function. We also study impact of clusters being more spread in the space on the value of the empty space hazard. Further we obtain asymptotic behavior of the empty space hazard functions at zero and at infinity.
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