We establish a functional central limit theorem for Ripley's K-function for two classes of point processes. One is the class of point processes having exponential decay of correlations and further satisfying a conditional m-dependence condition. The other is a family of Gibbs point processes. We illustrate the use of our theorem for goodness-of-fit tests in simulations.

翻译：我们为Ripley K- 函数的两类点进程设定了功能中心限值理论。 一种是具有相关关系指数衰减和进一步满足有条件依赖条件的点进程类别。 另一种是Gibbs点过程的组合。 我们用我们的理论来说明模拟中如何利用我们的理论进行良好的试验。