ABSTRACT
This chapter examines specific classes of point processes. The material is a mixture of general results and interesting special cases. Techniques range from martingale methods to strong approximation to sieves. The chapter presents an estimation of the mean measure and substitution of estimators of the mean measure to form empirical Laplace functionals and empirical zero-probability functionals specific to Poisson processes. It discusses application of strong approximation theorems for Poisson processes to empirical zero-probability functionals. The ease with which further testing problems can be posed for Poisson processes on general spaces is matched by the paucity of rigorous procedures available for addressing them in nonparametric settings. The chapter considers random measures with independent increments, whose Poisson cluster representation is given by Theorem and for which reasonably specific results can be developed.
