Complete $q$-order moment convergence of moving average processes under $\varphi $-mixing assumptions

Xing-Cai Zhou; Jin-Guan Lin

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 $\frac{1}{n} \sum_{1}^{n} 𝐟 (x_{i}^{n}) \cdot Z_{i}^{n}$ where the deterministic probability measure $\frac{1}{n} \sum_{1}^{n} δ_{x_{i}^{n}}$ converges weakly to a probability measure $R$ and ${(Z_{i}^{n})}_{i \in ℕ}$ are $ℝ^{d}$ -valued independent random variables whose distribution depends on $x_{i}^{n}$ and satisfies the following exponential moments condition: $sup_{i, n} 𝔼 e^{α^{*} | Z_{i}^{n} |} < + \infty forsome 0 < α^{*} < + \infty .$ 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 ${(S_{n})}_{n \geq 0}$ be a $ℤ$ -random walk and ${(ξ_{x})}_{x \in ℤ}$ 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 $𝒰_{n}, n \in ℕ$ , with values in $D [0, 1]$ the set of right continuous real-valued functions with left limits, defined by $\sum_{i, j = 0}^{[n t]} h (ξ_{S_{i}}, ξ_{S_{j}}), t \in [0, 1] .$ Statistical applications are presented, in particular we prove a strong law of large numbers for...

About the Lindeberg method for strongly mixing sequences

Emmanuel Rio (1997)

ESAIM: Probability and Statistics

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A correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”

Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2017)

Applications of Mathematics

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The authors provide a correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”.

Limiting behaviour of moving average processes based on a sequence of $ρ^{-}$ mixing and negatively associated random variables.

Budsaba, Kamon, Chen, Pingyan, Volodin, Andrei (2007)

Lobachevskii Journal of Mathematics

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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

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

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

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

About the Lindeberg method for strongly mixing sequences

A correction to “Some mean convergence and complete convergence theorems for sequences of m -linearly negative quadrant dependent random variables”

Limiting behaviour of moving average processes based on a sequence of ρ - mixing and negatively associated random variables.

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

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

A correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”

Limiting behaviour of moving average processes based on a sequence of $ρ^{-}$ mixing and negatively associated random variables.