On the accuracy of infinitely divisible approximation of $n$-fold convolutions of probability distributions

Applying the results of Zaitsev (1987) to specific symmetric distributions with slowly decreasing power tails, we obtained power estimates for the accuracy of the infinitely divisible approximation of the distributions of sums of $n$ i.i.d. random variables of the form $O(n^{-1+\varepsilon})$ with $\varepsilon$ arbitrarily close to zero.