Geodesic
Convergence to the Poisson process in a scheme of cummulative sums of dependent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 2, pp. 422-426 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using ideas of Theorem 1 [1], we find conditions for a sequence of processes, which are cumulative sums of indicators, to converge to a Poisson process. 
@article{TVP_1974_19_2_a18,
     author = {V. G. Mikhailov},
     title = {Convergence to the {Poisson} process in a~scheme of cummulative sums of dependent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {422--426},
     year = {1974},
     volume = {19},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a18/}
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V. G. Mikhailov. Convergence to the Poisson process in a scheme of cummulative sums of dependent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 2, pp. 422-426. http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a18/