A strictly stationary \(\beta\)-mixing process satisfying the central limit theorem but not the weak invariance principle

DOI10.1016/j.spa.2014.06.008zbMath1323.60041arXiv1304.7960OpenAlexW2016055004MaRDI QIDQ404595

Dalibor Volný, Davide Giraudo

Publication date: 4 September 2014

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

Full work available at URL: https://arxiv.org/abs/1304.7960

zbMATH Keywords

weak invariance principlecentral limit theoremmixing conditionsstrictly stationary process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Functional limit theorems; invariance principles (60F17)

Related Items (4)

On the invariance principle for reversible Markov chains ⋮ An improvement of the mixing rates in a counter-example to the weak invariance principle ⋮ Martingale-coboundary representation for stationary random fields ⋮ On limit theorems for fields of martingale differences

Cites Work

• On the central limit question under absolute regularity
• On the invariance principle of \(\rho\)-mixing sequences of random variables
• Asymptotic theory of weakly dependent stochastic processes
• On the weak invariance principle for non-adapted sequences under projective criteria
• A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
• The invariance principle for ϕ-mixing sequences
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