Abstract
Let {Xnk}, k = 1,2 kn; n = 1,2,..., be an array of random variables defined on a common probability space (Ω, F, P). If {Xnk} are row-wise independent, then there exists a quite satisfactory theory of the weak convergence of sums \(S_n ^\prime = \sum\limits_{k = 1}^{k_n } {X_{nk} .} \) One of the most reasonable trends in the analogous theory for dependent random variables is initiated by papers of Brown [2] and Dvoretzky [4], [5].
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Jakubowski, A. (1980). On Limit Theorems for Sums of Dependent Hilbert Space Valued Random Variables. In: Klonecki, W., Kozek, A., Rosiński, J. (eds) Mathematical Statistics and Probability Theory. Lecture Notes in Statistics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7397-5_13
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DOI: https://doi.org/10.1007/978-1-4615-7397-5_13
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