Displaying similar documents to “Convergence to zero and boundedness of operator-normed sums of random vectors with application to autoregression processes.”

On the strong convergence for weighted sums of asymptotically almost negatively associated random variables

Haiwu Huang, Guangming Deng, QingXia Zhang, Yuanying Jiang (2014)

Kybernetika

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Applying the moment inequality of asymptotically almost negatively associated (AANA, in short) random variables which was obtained by Yuan and An (2009), some strong convergence results for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of Zhou et al. (2011), Sung (2011, 2012) to the case of AANA random variables, respectively.

The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces

Nguyen Van Huan, Nguyen Van Quang (2012)

Kybernetika

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We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.

A central limit theorem for processes generated by a family of transformations

Marian Jabłoński

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Let τ n , n ≥ 0 be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let f n , n ≥ 0 be a sequence of elements of L 2 ( Ω , Σ , P ) with E f n = 0 . It is shown that the distribution of ( ∑ i = 0 n f i ∘ τ i ∘ . . . ∘ τ 0 ) ( D ( ∑ i = 0 n f i ∘ τ i ∘ . . . ∘ τ 0 ) ) - 1 tends to the normal distribution N(0,1) as n → ∞. 1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.