Geodesic
Generalized Marcinkiewicz laws for weighted dependent random vectors in Hilbert spaces
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 541-562

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The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=\sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;\, n\geq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto–Zipf distributions and multivariate log-gamma distributions.
Keywords: Marcinkiewicz laws of large numbers, dependent random vectors, Hilbert spaces, weighted sums. 
@article{TVP_2022_67_3_a6,
     author = {T. C. Son and L. V. Dung and D. T. Dat and T. T. Trang},
     title = {Generalized {Marcinkiewicz} laws for weighted dependent random vectors in {Hilbert} spaces},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {541--562},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a6/}
}
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T. C. Son; L. V. Dung; D. T. Dat; T. T. Trang. Generalized Marcinkiewicz laws for weighted dependent random vectors in Hilbert spaces. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 541-562. http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a6/