Geodesic
On limit distributions of a~statistic
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 2, pp. 367-374

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The random variables $$ \eta_n(t)=\sum_{i\le nt}a_ib_{x_i},\quad0\le t\le1, $$ are considered, where $a_1,\dots,a_n$ and $b_1,\dots,b_n$ are numerical sequences and $$ X= \begin{pmatrix} 12\hdots \\ x_1\hdots \end{pmatrix} $$ is a random permutation either from the class of all permutations or from the class of permutations with one cycle only. Conditions are obtained for finite dimensional distributions of $\eta_n(t)$ to converge to those of the limit processes. 
@article{TVP_1974_19_2_a9,
     author = {V. F. Kolchin and V. P. Chistyakov},
     title = {On limit distributions of a~statistic},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {367--374},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a9/}
}
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V. F. Kolchin; V. P. Chistyakov. On limit distributions of a~statistic. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 2, pp. 367-374. http://geodesic.mathdoc.fr/item/TVP_1974_19_2_a9/