A note on the almost sure approximation of weakly dependent random variables
A strong approximation theorem for Hilbert space valued martingales, due to \textit{G. J. Morrow} and the author [see Trans. Am. Math. Soc. 273, 231- 251 (1982; Zbl 0508.60014)], is improved. This result is then used to strengthen and, at the same time, to extend a recent strong approximation theorem for weakly dependent \({\mathbb{R}}^ d\)-valued random variables, due to \textit{E. Eberlein} [see Probability in Banach spaces IV, Proc. Semin., Oberwolfach 1982, Lect. Notes Math. 990, 84-91 (1983; Zbl 0515.60027)], to Hilbert space valued random variables.
almost sure approximation of weakly dependent random variables
scientific article; zbMATH DE number 3971859