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Limit theorems for dependent random variables. (English) Zbl 0845.60010
Lakshmikantham, V. (ed.), World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 1639-1650 (1996).
Summary: In many stochastic models, the assumption of independence among the random variables is not plausible. In fact, increases in some random variables are often related to decreases in other random variables and the assumption of negative dependence is more appropriate than independence assumptions. Weak and strong laws of large numbers are obtained for the weighted sum $\sum^\infty_{k = 1} a_{nk} X_{nk}$ under certain moment conditions on the random variables and suitable conditions on the weights where $\{X_{nk} : n,k \geq 1\}$ is an array of rowwise negatively dependent random variables and $\{a_{nk} : n,k \geq 1\}$ is a Toeplitz sequence. For the entire collection see [Zbl 0836.00032].

60B12Limit theorems for vector-valued random variables (infinite-dimensional case)