Doukhan, Paul; Klesov, Oleg; Lang, Gabriel Rates of convergence in some SLLN under weak dependence conditions. (English) Zbl 1240.60060 Acta Sci. Math. 76, No. 3-4, 683-695 (2010). Based on results of F. Móricz [Z.Wahrscheinlichkeitstheor.Verw.Geb.35, 299–314 (1976; Zbl 0314.60023)] and I. Fazekas and O. Klesov [Theory Probab. Appl. 45, No. 3, 436-449 (2000; Zbl 0991.60021)], the authors develop a general and quite effective method to derive convergence rate results in strong laws of large numbers for partial sums from suitable weighted maximal moment inequalities. The results obtained cover various weakly dependent situations, such as strong mixing cases, causal weak dependence, but also non-causal weak dependence. Moreover, convergence rates for kernel density and regression estimators of Nadaraya-Watson type are obtained via the same technique and also for a number of different dependence situations. Reviewer: Josef Steinebach (Köln) Cited in 3 Documents MSC: 60F15 Strong limit theorems 60F99 Limit theorems in probability theory 60G10 Stationary stochastic processes 62G07 Density estimation Keywords:strong law of large numbers; rate of convergence; maximal moment inequality; weak dependence; strong mixing; kernel density estimator; kernel regression estimator Citations:Zbl 0314.60023; Zbl 0991.60021 PDFBibTeX XMLCite \textit{P. Doukhan} et al., Acta Sci. Math. 76, No. 3--4, 683--695 (2010; Zbl 1240.60060)