Regular variation in the mean and stable limits for Poisson shot noise. (English) Zbl 1044.60013

Klüppelberg, Claudia; Mikosch, Thomas; Schärf, Anette

Bernoulli 9, No. 3, 467-496 (2003).

The authors study the limiting behaviour of Poisson shot noise when the limits are infinite-variance stable processes. In this context a sufficient condition for this convergence turns up which is closely related to multivariate regular variation. The authors also show that the latter condition is necessary and sufficient for the weak convergence of the point processes constructed from the normalized noise sequence and also for the weak convergence of its extremes.

Reviewer: Zdzislaw Rychlik (Lublin)

MSC:

60F05	Central limit and other weak theorems
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
60E07	Infinitely divisible distributions; stable distributions

Keywords:

Poisson random measure; infinitely divisible distribution; multivariate regular variation; self-similar process; stable process; weak convergence