Asymptotic properties of Schottky time series. (English. Ukrainian original) Zbl 0960.60036

Buldygin, V. V.; Il’jenko, A. B.

Theory Probab. Math. Stat. 59, 21-34 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 20-33 (1998).

The asymptotic behavior of time series which are values of Schottky effect process at discrete moments of times is investigated. Rates of convergence in the law of large numbers in \(L_{p}(\Omega)\) spaces are investigated. Estimates of probabilities of large deviations of sample means are proposed. The bounded law of the iterated logarithm and the central limit theorem are proved.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

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

Keywords:

time series; fractional processes; law of large numbers in \(L_{p}\)-spaces; large deviations; central limit theorem; law of the iterated logarithm