A Two-Parameter Maximal Ergodic Theorem with Dependence
McConnell, Terry R.
Ann. Probab., Tome 15 (1987) no. 4, p. 1569-1585 / Harvested from Project Euclid
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Let $X_1, X_2, \ldots$ and $Y_1, Y_2, \ldots$ be independent sequences of i.i.d. $U(0, 1)$ random variables. We characterize completely those Borel functions $F$ on $\lbrack 0, 1\rbrack^2$ for which the strong law of large numbers and the maximal ergodic theorem hold for the doubly indexed family $(1/nm)\sum_{i \leq n, j \leq m}F(X_i, Y_j)$.
Publié le : 1987-10-14
Classification:  Maximal ergodic theorem,  strong law of large numbers,  two-parameter martingales,  decoupling,  28D05,  60G60 
@article{1176991994,
     author = {McConnell, Terry R.},
     title = {A Two-Parameter Maximal Ergodic Theorem with Dependence},
     journal = {Ann. Probab.},
     volume = {15},
     number = {4},
     year = {1987},
     pages = { 1569-1585},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991994}
}

McConnell, Terry R. A Two-Parameter Maximal Ergodic Theorem with Dependence. Ann. Probab., Tome 15 (1987) no. 4, pp.  1569-1585. http://gdmltest.u-ga.fr/item/1176991994/