Displaying similar documents to “Complete q -order moment convergence of moving average processes under ϕ -mixing assumptions”

An invariance principle in L 2 [ 0 , 1 ] for non stationary ϕ -mixing sequences

Paulo Eduardo Oliveira, Charles Suquet (1995)

Commentationes Mathematicae Universitatis Carolinae

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Invariance principle in L 2 ( 0 , 1 ) is studied using signed random measures. This approach to the problem uses an explicit isometry between L 2 ( 0 , 1 ) and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a L 2 ( 0 , 1 ) version of the invariance principle in the case of ϕ -mixing random variables. Our result is not available in the D ( 0 , 1 ) -setting.

Large deviations for independent random variables – Application to Erdös-Renyi’s functional law of large numbers

Jamal Najim (2005)

ESAIM: Probability and Statistics

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A Large Deviation Principle (LDP) is proved for the family 1 n ∑ 1 n 𝐟 ( x i n ) · Z i n where the deterministic probability measure 1 n ∑ 1 n δ x i n converges weakly to a probability measure R and ( Z i n ) i ∈ ℕ are ℝ d -valued independent random variables whose distribution depends on x i n and satisfies the following exponential moments condition: sup i , n 𝔼 e α * | Z i n | < + ∞ forsome 0 < α * < + ∞ . In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

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...