| Title:
|
Strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables in metris spaces (English) |
| Author:
|
Quang, Nguyen Van |
| Author:
|
Nguyen, Pham Tri |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
6 |
| Year:
|
2016 |
| Pages:
|
669-684 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of the paper is to establish strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables in a convex combination space with or without compactly uniformly integrable condition. Some of our results are even new in the case of real random variables. (English) |
| Keyword:
|
strong law of large numbers |
| Keyword:
|
convex combination space |
| Keyword:
|
pairwise $m$-dependent |
| Keyword:
|
blockwise $m$-dependent |
| Keyword:
|
compactly uniformly integrable |
| MSC:
|
60B05 |
| MSC:
|
60F15 |
| MSC:
|
60G50 |
| idZBL:
|
Zbl 06674851 |
| idMR:
|
MR3572460 |
| DOI:
|
10.1007/s10492-016-0152-8 |
| . |
| Date available:
|
2016-11-26T20:45:56Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145915 |
| . |
| Reference:
|
[1] Bo, Z.: Marcinkiewicz-Zygmund law for sequences of blockwise $m$-dependent random variables.Statist. Probab. Lett. 38 (1998), 83-88. Zbl 0908.60009, MR 1629524, 10.1016/S0167-7152(97)00157-0 |
| Reference:
|
[2] Choi, B. D., Sung, S. H.: On convergence of $(S_n -ES_n)/n^{1/r}$, $1<r<2$, for pairwise independent random variables.Bull. Korean Math. Soc. 22 (1985), 79-82. MR 0826361 |
| Reference:
|
[3] Etemadi, N.: An elementary proof of the strong law of large numbers.Z. Wahrscheinlichkeitstheor. Verw. Geb. 55 (1981), 119-122. Zbl 0438.60027, MR 0606010, 10.1007/BF01013465 |
| Reference:
|
[4] Gaposhkin, V. F.: On the strong law of large numbers for blockwise independent and blockwise orthogonal random variables.Theory Probab. Appl. 39 677-684 (1994), translation from Teor. Veroyatn. Primen. Russian 39 804-812 (1994). Zbl 0847.60022, MR 1347654, 10.1137/1139053 |
| Reference:
|
[5] Móricz, F.: Strong limit theorems for blockwise $m$-dependent and blockwise quasi-orthogonal sequences of random variables.Proc. Am. Math. Soc. 101 (1987), 709-715. MR 0911038, 10.2307/2046676 |
| Reference:
|
[6] Quang, N. V., Thuan, N. T.: On the strong laws of large numbers for double arrays of random variables in convex combination spaces.Acta Math. Hung. 134 (2012), 543-564. Zbl 1265.60057, MR 2886225, 10.1007/s10474-011-0168-1 |
| Reference:
|
[7] Terán, P., Molchanov, I.: The law of large numbers in a metric space with a convex combination operation.J. Theor. Probab. 19 (2006), 875-898. Zbl 1113.60014, MR 2279607, 10.1007/s10959-006-0043-0 |
| Reference:
|
[8] Thanh, L. V.: Strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables.Bull. Inst. Math., Acad. Sin. 33 (2005), 397-405. Zbl 1084.60506, MR 2184437 |
| Reference:
|
[9] Thuan, N. T., Quang, N. V., Nguyen, P. T.: Complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces.Fuzzy Sets Syst. 250 (2014), 52-68. Zbl 1334.60041, MR 3223442 |
| . |
