Bounds for the probability generating functional of a Gibbs point   process
  We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity and higher order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation. 
Kaspar Stucki and Dominic Schuhmacher
math.PR math.ST stat.TH