A uniform central limit theorem for nonuniform \(\phi\)-mixing random fields

DOI10.1214/aop/1176990445zbMath0735.60034OpenAlexW2023563988MaRDI QIDQ1176151

Dongching Chen

Publication date: 25 June 1992

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176990445

zbMATH Keywords

limit theoremsstrictly stationary random fields\(\phi\)-mixing condition

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Convergence of probability measures (60B10) Functional limit theorems; invariance principles (60F17)

Related Items (21)

Exponential inequalities and functional central limit theorems for random fields ⋮ Strong laws for \(\alpha\)-mixing sequence processes indexed by sets ⋮ Invariance principles for self-similar set-indexed random fields ⋮ On the Rate of Complete Convergence for Weighted Sums of Arrays of Rowwise ϕ-Mixing Random Variables ⋮ Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields ⋮ Consistency and asymptotic normality of wavelet estimator in a nonparametric regression model ⋮ Asymptotics for the linear kernel quantile estimator ⋮ On complete convergence for weighted sums of \(\varphi \)-mixing random variables ⋮ A functional central limit theorem on non-stationary random fields with nested spatial structure ⋮ On the complete convergence for arrays of rowwise \({\psi}\)-mixing random variables ⋮ Exponential inequalities for sums of unbounded ϕ-mixing sequence and their applications ⋮ On a CLT for Gibbs fields and its functional version. ⋮ ON FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LINEAR RANDOM FIELDS WITH DEPENDENT INNOVATIONS ⋮ A Marcinkiewicz-Zygmund type strong law for weighted sums of \(\phi \)-mixing random variables and its applications ⋮ Equivalent conditions of complete moment and integral convergence for a class of dependent random variables ⋮ Moment inequality for \(\varphi \)-mixing sequences and its applications ⋮ Asymptotics for linear random fields ⋮ A central limit theorem for functions of stationary max-stable random fields on \(\mathbb{R}^d\) ⋮ Maximal inequalities for some dependent sequences and their applications ⋮ Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields. ⋮ The asymptotic properties of the estimators in a semiparametric regression model

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