Marcinkiewicz Laws and Convergence Rates in the Law of Large Numbers for Random Variables with Multidimensional Indices
Gut, Allan
Ann. Probab., Tome 6 (1978) no. 6, p. 469-482 / Harvested from Project Euclid
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Consider a set of independent identically distributed random variables indexed by $Z^d_+$, the positive integer $d$-dimensional lattice points, $d \geqq 2$. The classical Kolmogorov-Marcinkiewicz strong law of large numbers is generalized to this case. Also, convergence rates in the law of large numbers are derived, i.e., the rate of convergence to zero of, for example, the tail probabilities of the sample sums is determined.
Publié le : 1978-06-14
Classification:  i.i.d. random variables,  multidimensional index,  strong law of large numbers,  convergence rate,  60F15,  60G50 
@article{1176995531,
     author = {Gut, Allan},
     title = {Marcinkiewicz Laws and Convergence Rates in the Law of Large Numbers for Random Variables with Multidimensional Indices},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 469-482},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995531}
}

Gut, Allan. Marcinkiewicz Laws and Convergence Rates in the Law of Large Numbers for Random Variables with Multidimensional Indices. Ann. Probab., Tome 6 (1978) no. 6, pp.  469-482. http://gdmltest.u-ga.fr/item/1176995531/