On the \(L^p\)-convergence for multidimensional arrays of random variables (Q2575936)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(L^p\)-convergence for multidimensional arrays of random variables |
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On the \(L^p\)-convergence for multidimensional arrays of random variables (English)
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7 December 2005
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Summary: For a \(d\)-dimensional array of random variables \(\{X_n,n\in \mathbb{Z}^d_+\}\) such that \(\{|X_n|^p,n\in\mathbb{Z}^d_+\}\) is uniformly integrable for some \(0<p<2\), the \(L^p\)-convergence is established for the sums \((1/|n|^{1/p})(\sum_{j<n} (X_j-a_j))\), where \(a_j=0\) if \(0<p<1\), and \(a_j=EX_j\) if \(1\leq p<2\).
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