| Title:
|
An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes (English) |
| Author:
|
Morita, Takehiko |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
415-419 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
P. Samek and D. Volný, in the paper ``Uniqueness of a martingale-coboundary decomposition of a stationary processes" (1992), showed the uniqueness of martingale-coboundary decomposition of strictly stationary processes. The original proof is given by reducing the problem to the ergodic case. In this note we give another proof without such reduction. (English) |
| Keyword:
|
strictly stationary process |
| Keyword:
|
martingale-coboundary decomposition |
| MSC:
|
28D05 |
| MSC:
|
60G10 |
| MSC:
|
60G42 |
| idZBL:
|
Zbl 07144903 |
| idMR:
|
MR4034441 |
| DOI:
|
10.14712/1213-7243.2019.013 |
| . |
| Date available:
|
2019-10-29T13:03:16Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147855 |
| . |
| Reference:
|
[1] Billingsley P.: Ergodic Theory and Information.John Wiley & Sons, New York, 1965. MR 0192027 |
| Reference:
|
[2] Hall P., Heyde C. C.: Martingale Limit Theory and Its Application.Probability and Mathematical Statistics, Academic Press, New York, 1980. Zbl 0462.60045, MR 0624435 |
| Reference:
|
[3] Samek P., Volný D.: Uniqueness of a martingale-coboundary decomposition of a stationary processes.Comment. Math. Univ. Carolin. 33 (1992), no. 1, 113–119. MR 1173752 |
| Reference:
|
[4] Volný D.: Approximating martingales and the central limit theorem for strictly stationary processes.Stochastic Process. Appl. 44 (1993), no. 1, 41–74. MR 1198662, 10.1016/0304-4149(93)90037-5 |
| Reference:
|
[5] Walters P.: An Introduction to Ergodic Theory.Graduate Texts in Mathematics, 79, Springer, New York, 1982. Zbl 0958.28011, MR 0648108, 10.1007/978-1-4612-5775-2 |
| . |
