A note on a theorem of Berkes and Philipp for dependent sequences

We improve an almost sure invariance principle for f-mixing sequences of real random variables with finite (2 + [delta])th moment (0 < [delta] [less-than-or-equals, slant] 2) due to Berkes and Philipp (1979). The exponent of the slow logarithmic rate of mixing in that theorem is relaxed from 160/[delta] to (1 + [epsilon])(1 + 2/[delta]) and the undetermined quantities aN are replaced by N[sigma]2 for some [sigma] > 0.

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Year of publication:	1982
Authors:	Dabrowski, AndréRobert
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 1.1982, 2, p. 53-55
Publisher:	Elsevier
Keywords:	Almost sure invariance principles mixing random variables approximation theorems

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005223282