We consider empirical spectral processes indexed by classes of functions for the case of stationary point processes. Conditions for the measurability and equicontinuity of these processes and a weak convergence result are established. The results can be applied to the spectral analysis of point processes. In particular, we discuss the application to parametric and nonparametric spectral density estimation.
"Empirical Spectral Processes and Their Applications to Stationary Point Processes." Ann. Appl. Probab. 5 (4) 1161 - 1176, November, 1995. https://doi.org/10.1214/aoap/1177004610