Some convergence theorem for random variables in a Hilbert space with application (Q2925935)
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scientific article; zbMATH DE number 6362214
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some convergence theorem for random variables in a Hilbert space with application |
scientific article; zbMATH DE number 6362214 |
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29 October 2014
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asymptotically negative dependence
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convergence theorem
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Hilbert space
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linear process
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linear bounded operator
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almost sure convergence
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Rosenthal type inequality
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Some convergence theorem for random variables in a Hilbert space with application (English)
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In this paper, the notion of asymptotically negative dependence for random vectors with values in \({\mathbb R}^d, d\geq1\), is introduced and this notion is generalized to a Hilbert space. Moreover, conditions for almost sure convergence of negatively associated random vectors in a separable real Hilbert space \(H\) are obtained and this result is applied to a linear process generated by \(H\)-valued asymptotically negatively dependent random vectors.
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