The asymptotic theory for the sample mean of a marked point process in $d$ dimensions is established, allowing for the possibility that the underlying Poisson point process is inhomogeneous. A novel local block bootstrap method for resampling inhomogeneous Poisson marked point processes is introduced, and its consistency is proven for the sample mean and related statistics. Finite-sample simulations are carried out to complement the asymptotic results, and demonstrate the feasibility of the proposed methodology.
"Local block bootstrap for inhomogeneous Poisson marked point processes." Bernoulli 24 (1) 592 - 615, February 2018. https://doi.org/10.3150/16-BEJ889