Abstract
We derive a lower bound of L p norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X 1,..., X n with \(\mathbb{E}X_i \; = \;0\) under the boundedness condition ℙ{|X i | ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑ r⩾1 r 2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
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Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005.
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Sunklodas, J. A Lower Bound of L p Norms in the CLT for Strongly Mixing Random Variables. Lith Math J 45, 475–486 (2005). https://doi.org/10.1007/s10986-006-0009-z
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DOI: https://doi.org/10.1007/s10986-006-0009-z