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Complete convergence and convergence rates in Marcinkiewicz law of large numbers for random variables indexed by $$Z_+^d$$. (English) Zbl 0946.60027
The author proves some special convergence rate results in strong laws for multidimensionally indexed i.i.d. random variables; the components in the normalizations are raised to different powers. For example, instead of the standard $$P(|S_{n,m} |\geq \varepsilon n\cdot m)$$ the author considers $$P(|S_{n,m}|\geq\varepsilon n^{1/ \alpha}\cdot m^{1/ \beta})$$, where $$\alpha,\beta>0$$.
Reviewer: A.Gut (Uppsala)

##### MSC:
 60F15 Strong limit theorems 60G50 Sums of independent random variables; random walks