Martingale-coboundary representation for stationary random fields

DOI10.1142/S0219493718500119zbMath1378.60077OpenAlexW2595533519MaRDI QIDQ4598556

Dalibor Volný

Publication date: 21 December 2017

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493718500119

zbMATH Keywords

random fieldcentral limit theorems\(\mathbb{Z}^d\) actionorthomartingalemartingale-coboundary representation

Mathematics Subject Classification ID

Random fields (60G60) Martingales with discrete parameter (60G42) Functional limit theorems; invariance principles (60F17)

Related Items (8)

Invariance principle via orthomartingale approximation ⋮ Functional central limit theorem via nonstationary projective conditions ⋮ On limit theorems for fields of martingale differences ⋮ On Nörlund summation and ergodic theory, with applications to power series of Hilbert contractions ⋮ Joint and double coboundaries of commuting contractions ⋮ On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields ⋮ On the central limit theorem for stationary random fields under \({\mathbb{L}^1}\)-projective condition ⋮ Quenched invariance principles for orthomartingale-like sequences

Cites Work

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• The CLT for rotated ergodic sums and related processes
• A strictly stationary \(\beta\)-mixing process satisfying the central limit theorem but not the weak invariance principle
• Limit theorems for von Mises statistics of a measure preserving transformation
• A functional CLT for fields of commuting transformations via martingale approximation
• Comparison between criteria leading to the weak invariance principle
• An invariance principle for stationary random fields under Hannan's condition
• On moment conditions for normed sums of independent variables and martingale differences
• Approximating martingales and the central limit theorem for strictly stationary processes
• Large deviations for martingales.
• Central limit theorems for additive functionals of Markov chains.
• On the functional central limit theorem for stationary processes
• Martingale-coboundary representation for a class of random fields
• Orthomartingale-coboundary decomposition for stationary random fields
• A new condition for the invariance principle for stationary random fields
• CENTRAL LIMIT THEOREMS FOR SUPERLINEAR PROCESSES
• Exponential inequalities and functional central limit theorems for random fields
• On the central limit theorem and iterated logarithm law for stationary processes
• MARTINGALE APPROXIMATION OF NON-STATIONARY STOCHASTIC PROCESSES
• A central limit theorem for stationary random fields
• A central limit theorem for fields of martingale differences

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