The strong law of large numbers for martingales normalized by operators. (English. Ukrainian original) Zbl 0960.60021

Koval’, V. O.

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.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60F15	Strong limit theorems
60G42	Martingales with discrete parameter
62H12	Estimation in multivariate analysis
62J05	Linear regression; mixed models

Keywords:

martingales; strong law of large numbers

Citations:

Zbl 0960.60020