Comparison between criteria leading to the weak invariance principle

DOI10.1214/07-AIHP123zbMath1182.60010arXiv0805.3450OpenAlexW2164044255MaRDI QIDQ731668

Olivier Durieu, Dalibor Volný

Publication date: 8 October 2009

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.3450

zbMATH Keywords

weak invariance principlecentral limit theoremstationary processprojective criterionmartingale approximation

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Measure-preserving transformations (28D05) Functional limit theorems; invariance principles (60F17)

Related Items (12)

Limit theorems for weighted Bernoulli random fields under Hannan's condition ⋮ On the functional CLT for stationary Markov chains started at a point ⋮ Invariance principle via orthomartingale approximation ⋮ A quenched weak invariance principle ⋮ Martingale-coboundary representation for stationary random fields ⋮ A conditional CLT which fails for ergodic components ⋮ Hölderian weak invariance principle under the Maxwell and Woodroofe condition ⋮ On martingale approximations ⋮ An invariance principle for stationary random fields under Hannan's condition ⋮ CENTRAL LIMIT THEOREMS FOR SUPERLINEAR PROCESSES ⋮ A Fourth Moment Inequality for Functionals of Stationary Processes ⋮ Quenched Invariance Principles via Martingale Approximation

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