Geodesic
On limiting distributions for moduli of sequential differences of independent variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 693-707
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Let $(\xi,\eta)$ be a pair of independent equally distributed random variables, and $F(x)$ be their common distribution function. We define a sequence of pairs $(\xi_n,\eta_n)$ of independent equally distributed random variables with distribution functions $F_n(x)$: $$ F_1(x)=\mathbf\{|\xi-\eta|<x\},\quad F_{n+1}(x)=\mathbf P\{|\xi_n-\eta_n|<x\}, $$ and prove two theorems concerning the limiting behaviour of $F_n(x)$. 
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     author = {S. S. Vallander and I. A. Ibragimov and N. G. Lindtrop},
     title = {On limiting distributions for moduli of sequential differences of independent variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {693--707},
     year = {1969},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a7/}
}
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S. S. Vallander; I. A. Ibragimov; N. G. Lindtrop. On limiting distributions for moduli of sequential differences of independent variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 693-707. http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a7/