Summary
It is shown that for ϕ-mixing arrays of Banach space valued random vectors the central limit theorem implies the invariance principle. Applying this result to lattices of random variables a higher dimensional invariance principle under dependence assumptions is obtained.
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Dedicated to Professor Leopold Schmetterer
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Eberlein, E. An invariance principle for lattices of dependent random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 50, 119–133 (1979). https://doi.org/10.1007/BF00533633
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DOI: https://doi.org/10.1007/BF00533633