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- W4294611060 abstract "We prove that, for (adapted) stationary processes, the so-called Maxwell-Wood-roofe condition is sufficient for the law of the iterated logarithm and that it is optimal in some sense. We obtain a similar conclusion concerning the Marcinkiewicz-zygmund strong law of large numbers. Those results actually hold in the context of Banach valued stationary processes, including the case of $L^r$-valued random variables, with $1le r<infty$. In this setting we also prove the weak invariance principle, under a version of the Maxwell-Woodroofe condition, generalizing a result of Peligrad and Utev cite{PU}. Our results extend to non-adapted processes as well, and, partly to stationary processes arising from dynamical systems. The proofs make use of a new maximal inequality and of approximation by martingales, for which some of our results are also new." @default.
- W4294611060 created "2022-09-05" @default.
- W4294611060 creator A5082726825 @default.
- W4294611060 date "2014-03-04" @default.
- W4294611060 modified "2023-09-25" @default.
- W4294611060 title "Limit theorems under the Maxwell-Woodroofe condition in Banach spaces" @default.
- W4294611060 doi "https://doi.org/10.48550/arxiv.1403.0772" @default.
- W4294611060 hasPublicationYear "2014" @default.
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