Several large deviation estimations for the Poisson point processes.(English)Zbl 0832.60035

Summary: We obtain the large deviation estimations for the Poisson point processes in the following three limit behaviors: (1) high density behavior, (2) low density behavior (a counterpart of Schilder’s theorem in the Poisson case) and (3) scaling limit behavior.

MSC:

 60F10 Large deviations 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)