A compact LIL for martingales in \(2\)-smooth Banach spaces with applications

DOI10.3150/13-BEJ571zbMath1321.60057arXiv1209.3680MaRDI QIDQ2345125

Christophe Cuny

Publication date: 19 May 2015

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.3680

zbMATH Keywords

Marcinkiewicz-Zygmund strong law of large numbersstrong invariance principleBanach-space-valued martingalescompact law of iterated logarithm\(\phi\)-mixing sequences

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Stationary stochastic processes (60G10) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items

Study of almost everywhere convergence of series by mean of martingale methods, Limit theorems for U-statistics of Bernoulli data, Bound on the maximal function associated to the law of the iterated logarithms for Bernoulli random fields, Limit theorems for Markov chains by the symmetrization method, Convergence of series of conditional expectations, Limit theorems for the left random walk on \(\mathrm{GL}_{d}(\mathbb{R})\), A functional CLT for fields of commuting transformations via martingale approximation, Maximal function associated to the bounded law of the iterated logarithms via orthomartingale approximation

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