Displaying similar documents to “Central limit theorem for sampled sums of dependent random variables”

Complete convergence of weighted sums for arrays of rowwise ϕ -mixing random variables

Xinghui Wang, Xiaoqin Li, Shuhe Hu (2014)

Applications of Mathematics

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In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise ϕ -mixing random variables, and the Baum-Katz-type result for arrays of rowwise ϕ -mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of ϕ -mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).

Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-Plantard, Véronique Ladret (2005)

ESAIM: Probability and Statistics

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Let ( S n ) n ≥ 0 be a ℤ -random walk and ( ξ x ) x ∈ ℤ be a sequence of independent and identically distributed ℝ -valued random variables, independent of the random walk. Let h be a measurable, symmetric function defined on ℝ 2 with values in ℝ . We study the weak convergence of the sequence 𝒰 n , n ∈ ℕ , with values in D [ 0 , 1 ] the set of right continuous real-valued functions with left limits, defined by ∑ i , j = 0 [ n t ] h ( ξ S i , ξ S j ) , t ∈ [ 0 , 1 ] . Statistical applications are presented, in particular we prove a strong law of large numbers for...