| Title:
|
An invariance principle in $L^2[0,1]$ for non stationary $\varphi$-mixing sequences (English) |
| Author:
|
Oliveira, Paulo Eduardo |
| Author:
|
Suquet, Charles |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
293-302 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Invariance principle in $L^2(0,1)$ is studied using signed random measures. This approach to the problem uses an explicit isometry between $L^2(0,1)$ and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a $L^2(0,1)$ version of the invariance principle in the case of $\varphi$-mixing random variables. Our result is not available in the $D(0,1)$-setting. (English) |
| Keyword:
|
reproducing kernel Hilbert space |
| Keyword:
|
random measure |
| Keyword:
|
invariance principle |
| Keyword:
|
$\varphi$-mixing |
| MSC:
|
60F17 |
| MSC:
|
60G57 |
| idZBL:
|
Zbl 0836.60031 |
| idMR:
|
MR1357531 |
| . |
| Date available:
|
2009-01-08T18:18:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118758 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| . |
