| Title:
|
Complete convergence in mean for double arrays of random variables with values in Banach spaces (English) |
| Author:
|
Son, Ta Cong |
| Author:
|
Thang, Dang Hung |
| Author:
|
Dung, Le Van |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
177-190 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The rate of moment convergence of sample sums was investigated by Chow (1988) (in case of real-valued random variables). In 2006, Rosalsky et al. introduced and investigated this concept for case random variable with Banach-valued (called complete convergence in mean of order $p$). In this paper, we give some new results of complete convergence in mean of order $p$ and its applications to strong laws of large numbers for double arrays of random variables taking values in Banach spaces. (English) |
| Keyword:
|
complete convergence in mean |
| Keyword:
|
double array of random variables with values in Banach space |
| Keyword:
|
martingale difference double array |
| Keyword:
|
strong law of large numbers |
| Keyword:
|
$p$-uniformly smooth space |
| MSC:
|
60B11 |
| MSC:
|
60B12 |
| MSC:
|
60F15 |
| MSC:
|
60F25 |
| idZBL:
|
Zbl 06362220 |
| idMR:
|
MR3183471 |
| DOI:
|
10.1007/s10492-014-0048-4 |
| . |
| Date available:
|
2014-03-20T08:19:59Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143628 |
| . |
| Reference:
|
[1] Adler, A., Rosalsky, A.: Some general strong laws for weighted sums of stochastically dominated random variables.Stochastic Anal. Appl. 5 (1987), 1-16. Zbl 0617.60028, MR 0882694, 10.1080/07362998708809104 |
| Reference:
|
[2] Chow, Y. S.: On the rate of moment convergence of sample sums and extremes.Bull. Inst. Math., Acad. Sin. 16 (1988), 177-201. Zbl 0655.60028, MR 1089491 |
| Reference:
|
[3] Dung, L. V., Ngamkham, T., Tien, N. D., Volodin, A. I.: Marcinkiewicz-Zygmund type law of large numbers for double arrays of random elements in Banach spaces.Lobachevskii J. Math. 30 (2009), 337-346. Zbl 1227.60008, MR 2587856, 10.1134/S1995080209040118 |
| Reference:
|
[4] Hoffmann-Jørgensen, J., Pisier, G.: The law of large numbers and the central limit theorem in Banach spaces.Ann. Probab. 4 (1976), 587-599. Zbl 0368.60022, MR 0423451, 10.1214/aop/1176996029 |
| Reference:
|
[5] Pisier, G.: Martingales with values in uniformly convex spaces.Isr. J. Math. 20 (1975), 326-350. Zbl 0344.46030, MR 0394135, 10.1007/BF02760337 |
| Reference:
|
[6] Rosalsky, A., Thanh, L. V., Volodin, A. I.: On complete convergence in mean of normed sums of independent random elements in Banach spaces.Stochastic Anal. Appl. 24 (2006), 23-35. Zbl 1087.60009, MR 2198535, 10.1080/07362990500397319 |
| Reference:
|
[7] Scalora, F. S.: Abstract martingale convergence theorems.Pac. J. Math. 11 (1961), 347-374. Zbl 0114.07702, MR 0123356, 10.2140/pjm.1961.11.347 |
| . |
