Some conclusions from the general lemma on the probabilities of large deviations for random fields with perturbations. (Russian) Zbl 0577.60027

Akhmedov, S.

Teor. Veroyatn. Mat. Stat. 29, 7-10 (1983).

Sums \(Y_ k\), \(k=1,2,..\). of weakly dependent random fields are considered. The weak dependence is expressed by the mixing coefficient. Under various conditions, concerning the mixing coefficients, moments and semivariants of the \(Y_ k\), the convergence rate in a known central limit theorem for \(Y_ k\) and the asymptotic expansion of the probabilities of large deviations are obtained. For this, the general lemma on the probabilities of large deviations is used.

Reviewer: C.Baldauf

MSC:

60F10	Large deviations
60G50	Sums of independent random variables; random walks
60F15	Strong limit theorems

Keywords:

weakly dependent random fields; mixing coefficient; convergence rate; central limit theorem; asymptotic expansion