The asymptotic behaviour of sample means of shot noise processes. (English. Ukrainian original) Zbl 0998.60030

Il’jenko, A. B.

Theory Probab. Math. Stat. 64, 63-73 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 57-65 (2001).

Let \(q(t)\) be a shot noise process defined by the Lévy process without Gaussian component. Asymptotic properties of sample averages of the type \(\overline q(T) =(1/T)\int _0^T q(t) dt\) are investigated. For instance, conditions which provide the central limit theorem and the law of iterated logarithm for \(\overline q(T)\) are discussed.

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60F25	\(L^p\)-limit theorems
60F10	Large deviations
60G10	Stationary stochastic processes
60F05	Central limit and other weak theorems

Keywords:

stochastic processes with independent increments; shot noise processes; sample average; large deviations; central limit theorem; law of iterated logarithm; moments characterization