Strong laws of large numbers for sequences of blockwise and pairwise m -dependent random variables in metris spaces

Nguyen Van Quang; Pham Tri Nguyen

Applications of Mathematics (2016)

  • Volume: 61, Issue: 6, page 669-684
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Quang, Nguyen Van, and Nguyen, Pham Tri. "Strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables in metris spaces." Applications of Mathematics 61.6 (2016): 669-684. <http://eudml.org/doc/287533>.

@article{Quang2016,
abstract = {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.},
author = {Quang, Nguyen Van, Nguyen, Pham Tri},
journal = {Applications of Mathematics},
keywords = {strong law of large numbers; convex combination space; pairwise $m$-dependent; blockwise $m$-dependent; compactly uniformly integrable; strong law of large numbers; convex combination space; pairwise $m$-dependent; blockwise -dependent; compactly uniformly integrable},
language = {eng},
number = {6},
pages = {669-684},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables in metris spaces},
url = {http://eudml.org/doc/287533},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Quang, Nguyen Van
AU - Nguyen, Pham Tri
TI - Strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables in metris spaces
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 6
SP - 669
EP - 684
AB - 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.
LA - eng
KW - strong law of large numbers; convex combination space; pairwise $m$-dependent; blockwise $m$-dependent; compactly uniformly integrable; strong law of large numbers; convex combination space; pairwise $m$-dependent; blockwise -dependent; compactly uniformly integrable
UR - http://eudml.org/doc/287533
ER -

References

top
  1. Bo, Z., 10.1016/S0167-7152(97)00157-0, Statist. Probab. Lett. 38 (1998), 83-88. (1998) Zbl0908.60009MR1629524DOI10.1016/S0167-7152(97)00157-0
  2. Choi, B. D., Sung, S. H., On convergence of ( S n - E S n ) / n 1 / r , 1 < r < 2 , for pairwise independent random variables, Bull. Korean Math. Soc. 22 (1985), 79-82. (1985) MR0826361
  3. Etemadi, N., 10.1007/BF01013465, Z. Wahrscheinlichkeitstheor. Verw. Geb. 55 (1981), 119-122. (1981) Zbl0438.60027MR0606010DOI10.1007/BF01013465
  4. Gaposhkin, V. F., 10.1137/1139053, Theory Probab. Appl. 39 677-684 (1994), translation from Teor. Veroyatn. Primen. Russian 39 804-812 (1994). (1994) Zbl0847.60022MR1347654DOI10.1137/1139053
  5. Móricz, F., 10.2307/2046676, Proc. Am. Math. Soc. 101 (1987), 709-715. (1987) MR0911038DOI10.2307/2046676
  6. Quang, N. V., Thuan, N. T., 10.1007/s10474-011-0168-1, Acta Math. Hung. 134 (2012), 543-564. (2012) Zbl1265.60057MR2886225DOI10.1007/s10474-011-0168-1
  7. Terán, P., Molchanov, I., 10.1007/s10959-006-0043-0, J. Theor. Probab. 19 (2006), 875-898. (2006) Zbl1113.60014MR2279607DOI10.1007/s10959-006-0043-0
  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. (2005) Zbl1084.60506MR2184437
  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. (2014) Zbl1334.60041MR3223442

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.