Geodesic
The rate of normal approximation for the distribution of the number of multiple repetitions of characters in a stationary random sequence
Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 11-13

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We study the asymptotic normality of the number of $r$-fold characters repetitions in a segment of length $n$ of a strictly stationary random sequence with values in a finite set that satisfies the uniformly strong mixing condition. It is shown that if there exists a number $\alpha> 0$ such that the uniformly strong mixing coefficient $\varphi(t)$ decreases as $t^{-6-\alpha}$, then the distance in the uniform metric between the distribution function of the standardized number of repetitions of multiplicity $r$ and the distribution function of the standard normal law decreases at a rate of $O(n^{-\delta})$ for any $\delta \in (0,\alpha (32+4\alpha)^{ -1})$ with increasing of segment length $n$.
Keywords: multiple repetitions, dependent random variables, uniformly strong mixing, normal approximation, convergence rate estimate. 
@article{PDMA_2022_15_a2,
     author = {V. G. Mikhailov and N. M. Mezhennaya},
     title = {The rate of normal approximation for the distribution of the number of multiple repetitions of characters in a stationary random sequence},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {11--13},
     publisher = {mathdoc},
     number = {15},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2022_15_a2/}
}
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V. G. Mikhailov; N. M. Mezhennaya. The rate of normal approximation for the distribution of the number of multiple repetitions of characters in a stationary random sequence. Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 11-13. http://geodesic.mathdoc.fr/item/PDMA_2022_15_a2/