A proof of a non-commutative central limit theorem by the Lindeberg method.

Kargin, Vladislav

Displaying similar documents to “A proof of a non-commutative central limit theorem by the Lindeberg method.”

On convergence for sequences of pairwise negatively quadrant dependent random variables

Yongfeng Wu, Guangjun Shen (2014)

Applications of Mathematics

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In this paper, some new results on complete convergence and complete moment convergence for sequences of pairwise negatively quadrant dependent random variables are presented. These results improve the corresponding theorems of S. X. Gan, P. Y. Chen (2008) and H. Y. Liang, C. Su (1999).

Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables

Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2013)

Applications of Mathematics

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The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of $m$ -linearly negative quadrant dependent random variables ( $m = 1, 2, \dots$ ). For a sequence of $m$ -linearly negative quadrant dependent random variables ${X_{n}, n \geq 1}$ and $1 < p < 2$ (resp. $1 \leq p < 2$ ), conditions are provided under which $n^{- 1 / p} \sum_{k = 1}^{n} (X_{k} - E X_{k}) \to 0$ in $L^{1}$ (resp. in $L^{p}$ ). Moreover, for $1 \leq p < 2$ , conditions are provided under which $n^{- 1 / p} \sum_{k = 1}^{n} (X_{k} - E X_{k})$ converges completely to $0$ . The current work extends some results of Pyke and Root (1968) and it extends and...

A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system

Kangkang Wang (2009)

Czechoslovak Mathematical Journal

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In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system...