Geodesic
Approximation of convolutions by accompanying laws under the existence of moment of low orders
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 135-141

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It is shown that if a one-dimensional distribution $F$ has finite moment of the order $1+\beta$ for some $\beta$, $\frac12\le\beta\le1$, then the rate of approximation of the $n$-fold convolution $F^n$ by accompanying laws is $O(n^{-\frac12})$. Moreover, if, in addition, $\mathbf E\xi^2=\infty$, $\frac12\beta1$, then this rate of approximation is $o(n^{-\frac12})$. The question about the true rate of approximation of $F^n$ by infinitely divisible and accompanying laws is discussed. Bibl. 27 titles. 
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     author = {A. Yu. Zaitsev},
     title = {Approximation of convolutions by accompanying laws under the existence of moment of low orders},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--141},
     publisher = {mathdoc},
     volume = {228},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a10/}
}
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A. Yu. Zaitsev. Approximation of convolutions by accompanying laws under the existence of moment of low orders. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 135-141. http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a10/