The asymptotic variance of the sample mean of a homogeneous Poisson marked point process has been studied in the literature, but confusion has arisen as to the correct expression due to some technical intricacies. This note sets the record straight with regards to the variance of the sample mean. In addition, a central limit theorem in the general d-dimensional case is also established.
"The correct asymptotic variance for the sample mean of a homogeneous Poisson marked point process." J. Appl. Probab. 50 (3) 889 - 892, September 2013. https://doi.org/10.1239/jap/1378401244