Geodesic
Limit theorem for some functionals of random walks
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 483-492

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Let $\xi_,\xi_2,\dots,\xi_n,\dots$ be a sequence of independent random variables with the same distributions, $S_n=\sum_{j=1}^n\xi_j$ and let $f(x,y)$ be a measurable function. Limit theorems for the distributions of sums $\sum_{j=0}^{n-1}\sum_{k=0}^{n-1}S(S_jS_k)$ are obtained. 
@article{TVP_1967_12_3_a6,
     author = {G. N. Sytaya},
     title = {Limit theorem for some functionals of random walks},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {483--492},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a6/}
}
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G. N. Sytaya. Limit theorem for some functionals of random walks. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 483-492. http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a6/