Displaying similar documents to “On convergence for sequences of pairwise negatively quadrant dependent random variables”

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 , ⋯ ). For a sequence of m -linearly negative quadrant dependent random variables { X n , n ≥ 1 } and 1 < p < 2 (resp. 1 ≤ p < 2 ), conditions are provided under which n - 1 / p ∑ k = 1 n ( X k - E X k ) → 0 in L 1 (resp. in L p ). Moreover, for 1 ≤ p < 2 , conditions are provided under which n - 1 / p ∑ 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...

On a quadratically convergent method using divided differences of order one under the gamma condition

Ioannis Argyros, Hongmin Ren (2008)

Open Mathematics

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We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an equation in a Banach space setting [4, 5, 7]. Recently in [4, 5, 7], using Lipschitz conditions, and a Newton-Kantorovich type approach, we provided a local as well as a semilocal convergence analysis for this method which compares favorably to other methods using two function evaluations such as the Steffensen’s method [1, 3, 13]. Here, we provide...

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...