Geodesic
On a complete moment convergence in precise asymptotics
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 180-188
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Liu and Lin (Statist. Probab. Lett. 2006) introduced a kind of complete moment convergence which includes the traditional one as a special case. We continue these investigations to make them somewhat more general and sharp. 
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L. V. Rozovsky. On a complete moment convergence in precise asymptotics. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 180-188. http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a11/

[1] W. D. Liu, Z. Y. Lin, “Precise asymptotics for a new kind of complete moment convergence”, Stat. Probab. Lett., 76:16 (2006), 1787–1799 | DOI | MR

[2] L. T. Kong, H. S. Dai, “Convergence rates in precise asymptotics for a kind of complete moment convergence”, Stoch. Dynamics, 17:2 (2017), 1750015 | DOI | MR

[3] Y. Zhang, “A note on the convergence rates in precise asymptotics”, J. Ineq. Appl., 15 (2019) | MR

[4] L. V. Rozovskii, “Summy nezavisimykh sluchainykh velichin s konechnymi dispersiyami – umerennye ukloneniya i neravnomernye otsenki v TsPT”, Zap. nauchn. semin. POMI, 311, 2004, 242–259

[5] L. V. Rozovsky, “One more on the convergence rates in precise asymptotics”, Statist. Prob. Lett., 171 (2021), 109023 | DOI | MR