×

Vitesse de convergence dans le théorème de limite centrale pour des champs mélangeants satisfaisant des hypothèses de moment faibles. (Rates in the central limit theorem for mixing random fields satisfying low moment assumptions). (French) Zbl 0719.60020

Summary: We give an expression for the rate of convergence in the central limit theorem for mixing random fields assuming low moment assumptions, e.g. E \(X^ 2 \ln^{\delta}_+(X)<\infty\). We use, for it, a truncation in the first author’s results [Sov. Math., Dokl. 34, No.3, 416-419 (1987); translation from Dokl. Akad. Nauk SSSR 291, 22-25 (1986; Zbl 0665.60028)] leading to results analogous to those well-known in the independent case [see V. V. Petrov, Limit theorems for the sums of independent random variables (1987; Zbl 0621.60022)].

MSC:

60F05 Central limit and other weak theorems
60G60 Random fields
PDFBibTeX XMLCite