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- Author or Editor: Rafał Kulik x
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In this article we prove a weak invariance principle for a strictly stationary
φ
-mixing sequence {
X
j
}
j≧1
, whose truncated variance function \documentclass{aastex}
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\begin{document}
$$L(x): = EX_1^2 1_{\{ |X_1 | \leqq _x \} }$$
\end{document} is slowly varying at ∞ and mixing coefficients satisfy the logarithmic growth condition: Σ
n
≧1
φ
1/2
(2
n
) < ∞. This will be done under the condition that \documentclass{aastex}
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$$\mathop {\lim }\limits_n Var\left( {\sum\limits_{j = 1}^n {\hat X_j } } \right)/\left[ {\sum\limits_{j = 1}^n {Var (\hat X_j )} } \right] = \beta ^2$$
\end{document} exists in (0, ∞), where \documentclass{aastex}
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\begin{document}
$$\hat X_j = X_j I_{\{ |X_j | \leqq \eta _j \} }$$
\end{document} and
η
n
2
∼
nL
(
η
n
).
