Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields.

DOI10.1016/S0304-4149(02)00178-3zbMath1075.60506MaRDI QIDQ2574529

Mohamed El Machkouri

Publication date: 29 November 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

invariance principlemetric entropymartingale difference random fieldsmixing random fieldsKahane-Khinchin inequalities

Mathematics Subject Classification ID

Random fields (60G60) Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Nonparametric regression estimation for random fields in a fixed-design ⋮ Self‐normalization for Spatial Data ⋮ Randomized multivariate central limit theorems for ergodic homogeneous random fields ⋮ Almost sure behavior of functionals of stationary Gibbs point processes

Cites Work

• A uniform central limit theorem for set-indexed partial-sum processes with finite variance
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• A uniform central limit theorem for nonuniform \(\phi\)-mixing random fields
• Gibbs measures and phase transitions
• A maximal inequality and dependent strong laws
• Mixing: Properties and examples
• Central limit theorem for random processes with sample paths in exponential Orlicz spaces
• Asymptotic theory of weakly dependent stochastic processes
• Best constants in Kahane-Khintchine inequalities in Orlicz spaces
• Sample functions of the Gaussian process
• Law of the iterated logarithm for set-indexed partial sum processes with finite variance
• Exponential inequalities and functional central limit theorems for random fields
• The Invariance Principle for a Lattice of Random Variables
• Contributions to Central Limit Theory for Dependent Variables
• Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters
• Some Limit Theorems for Stationary Processes
• A central limit theorem for stationary random fields
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