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The strong law of large numbers for martingales normalized by operators. (English. Ukrainian original) Zbl 0960.60021
Theory Probab. Math. Stat. 59, 67-75 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 66-74 (1998).
Strong laws of large numbers with operator normalization for sums of independent random vectors and martingales have been studied in many papers (see, for example, the paper reviewed above). It was assumed that martingales have moments of order \(\nu\in [1,2].\) In this paper the case \(\nu\in [2,+\infty)\) is considered. Namely, sufficient conditions for the fulfilment of the strong law of large numbers for martingales with operator normalization in \(R^{n}\) which have moment of order \(\nu\in [2,+\infty)\) are established.
60F15 Strong limit theorems
60G42 Martingales with discrete parameter
62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models