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Zbl 0798.60027
Rio, Emmanuel
Covariance inequalities for strongly mixing processes. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 29, No.4, 587-597 (1993). ISSN 0246-0203

It is proved that $$\bigl \vert \text {cov} (X,Y) \bigr \vert \le 2 \int\sp{2\alpha}\sb 0 Q\sb x (u)Q\sb y (u)du$$, where $Q\sb x(u) = \inf \{t : P(\vert x \vert>t) \le u\}$ and $\alpha$ is the strong mixing coefficient between two $\sigma$-fields generated respectively by real- valued random variables $X$ and $Y$. This inequality, extending e.g. Davydov's one, is sharp, up to a constant factor. It is applied to obtain bounds of the variance of sums of strongly mixing processes and fields. In a recent paper by {\it P. Doukhan}, {\it P. Massart} and the author [ibid. 30, No. 1, 63-82 (1994; Zbl 0790.60037)] it is used also to prove the functional CLT for strongly mixing processes.
[A.V.Bulinskij (Moskva)]

MSC 2000:: *60F05 Weak limit theorems
60F17 Functional limit theorems

Keywords: covariance inequalities; strongly mixing processes; functional central limit theorem for strongly mixing processes

Citations: Zbl 0790.60037

Cited in: Zbl 1075.60012 Zbl 1005.62035 Zbl 0969.60026 Zbl 0835.60017

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