Geodesic
Limit theorems for the scheme of series for weakly dependent variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 888-897

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The paper provides necessary and sufficient conditions for convergence of distributions of sums of weakly dependent random variables to the preassigned infinitely divisible distributions. Given in terms of individual summands and so-called normalizing sequences, the results obtained extend to the series scheme their counterparts established previously for stationary sequences.
Keywords: scheme of series, infinitely divisible distributions, weakly dependent variables, conditions of strong mixing, uniformly strong mixing and $\lambda$-mixing. 
@article{TVP_1995_40_4_a15,
     author = {A. G. Grin'},
     title = {Limit theorems for the scheme of series for weakly dependent variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {888--897},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a15/}
}
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A. G. Grin'. Limit theorems for the scheme of series for weakly dependent variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 888-897. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a15/