A functional CLT for fields of commuting transformations via martingale approximation

DOI10.1007/s10958-016-3145-yzbMath1376.60055OpenAlexW2542935414MaRDI QIDQ504002

Christophe Cuny, Dalibor Volný, Jérôme Dedecker

Publication date: 24 January 2017

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-016-3145-y

zbMATH Keywords

Brownian sheetmartingale approximation\(L^{2}\)-modulus

Mathematics Subject Classification ID

Random fields (60G60) Martingales with continuous parameter (60G44) Functional limit theorems; invariance principles (60F17)

Related Items (11)

On the weak invariance principle for non-adapted stationary random fields under projective criteria ⋮ An exponential inequality for orthomartingale difference random fields and some applications ⋮ Martingale-coboundary representation for stationary random fields ⋮ Functional central limit theorem via nonstationary projective conditions ⋮ On the quenched central limit theorem for stationary random fields under projective criteria ⋮ Central limit theorem for Fourier transform and periodogram of random fields ⋮ On the normal approximation for random fields via martingale methods ⋮ Martingale approximations for random fields ⋮ Randomized multivariate central limit theorems for ergodic homogeneous random fields ⋮ On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields ⋮ Quenched invariance principles for orthomartingale-like sequences

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