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Zbl 0949.60049
Dedecker, Jérôme; Rio, Emmanuel
On the functional central limit theorem for stationary processes. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 36, No.1, 1-34 (2000). ISSN 0246-0203

The Donsker-type invariance principle is proved for stationary processes with second order moments which satisfy the usual central limit theorem under conditions such as $\alpha$-mixing, $\beta$-mixing as well as stationary Markov chains. In the latter case, some examples of non-irreducible and non-$\alpha$-mixing chains to which these results apply are presented.
[N.Leonenko (Ky{\" i}v)]

MSC 2000:: *60F17 Functional limit theorems
60G10 Stationary processes

Keywords: strictly stationary process; invariance principle; strong mixing; Markov chains

Cited in: Zbl 1182.60010

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