| Title:
|
On a characterization of orthogonality with respect to particular sequences of random variables in $L^2$ (English) |
| Author:
|
Triacca, Umberto |
| Author:
|
Volodin, Andrei |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
329-335 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space $L^2(\Omega ,\mathcal F,\mathbb P)$ of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of $L^2(\Omega ,\mathcal F,\mathbb P)$) to be orthogonal to some other sequence in $L^2(\Omega ,\mathcal F,\mathbb P)$. The result obtained is interesting from the point of view of the time series analysis, since it can be applied to a class of sequences random variables that exhibit a monotonically increasing variance. An application to ergodic theorem is also provided. (English) |
| Keyword:
|
Hilbert space |
| Keyword:
|
orthogonality |
| Keyword:
|
ergodic theorem |
| MSC:
|
60F15 |
| MSC:
|
60G50 |
| idZBL:
|
Zbl 1224.60053 |
| idMR:
|
MR2737940 |
| DOI:
|
10.1007/s10492-010-0024-6 |
| . |
| Date available:
|
2010-07-20T13:51:23Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140403 |
| . |
| Reference:
|
[1] Wermuth, E. M. E.: A remark on equidistance in Hilbert spaces.Linear Algebra Appl. 236 (1996), 105-111. Zbl 0843.46015, MR 1375608 |
| . |
