Geodesic
Limit theorems for randomized stationary processes and stable laws
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 92-104

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Davydov Yu. A., Rahmankin D. S. Limit theorems for randomized stationary processes and stable laws. \smallbreak \nopagebreak The goal of this work is to find conditions under which partial sums of strictly stationary sequences are attracted to a non-Gaussian stable limit. In contrast to the results available in the literature, we come away from the traditional methods and use a new approach based on randomization of the initial data. His effectiveness is confirmed by examples. Thus, it turned out that in the case of uniformly strong mixing, without any conditions on the mixing coefficient, the convergence of randomized sums occurs whenever when the marginal distribution lies in the area of attraction of a stable law. 
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     title = {Limit theorems for randomized stationary processes and stable laws},
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Yu. A. Davydov; D. S. Rahmankin. Limit theorems for randomized stationary processes and stable laws. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 92-104. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a6/