A strong limit theorem for sequences of blockwise and pairwise m-dependent random variables

다국어 초록 (Multilingual Abstract)

In this paper, we establish a Marcinkiewicz-Zygmund type strong law for sequences of blockwise and pairwise m-dependent random variables. The sharpness of the results is illustrated by an example.

참고문헌 (Reference)

1 성수학, "Weak laws of large numbers for arrays under a condition of uniform integrability" 대한수학회 45 (45): 289-300, 2008

2 A. Wigderson, "The amazing power of paiwise independence" 645-647, 1994

3 M. Harber, "Testing for pairwise independence" 42 : 429-435, 1986

4 A. Rosalsky, "Strong stability of normed weighted sums of pairwise i.i.d. random vari- ables" 15 (15): 203-219, 1987

5 D. Li, "Strong limit theorems for blockwise m-dependent random vari- ables and a generalization of the conjectures of Moricz" 12 (12): 192-201, 1991

6 F. Moricz, "Strong limit theorems for blockwise m-dependent and blockwise quasi-orthogonal sequences of random variables" 101 (101): 709-715, 1987

7 L. V. Thanh, "Strong laws of large numbers for sequences of blockwise and pairwise m- dependent random variables" 33 (33): 397-405, 2005

8 I. Fazekas, "Strong laws of large numbers for pairwise independent random variables with multidimensional indices" 53 (53): 149-161, 1998

9 A. Adler, "Some strong laws of large numbers for sums of random elements" 20 (20): 335-357, 1992

10 F. Moricz, "SLLN and convergence rates for nearly orthogonal sequences of random variables" 95 (95): 287-294, 1985

11 G. L. O'Brien, "Pairwise independent random variables" 8 (8): 170-175, 1980

12 S. Geisser, "Pairwise independence of jointly dependent variables" 33 : 290-291, 1962

13 A. Martikainen, "On the strong law of large numbers for sums of pairwise independent random variables" 25 (25): 21-26, 1995

14 D. Li, "On the strong law of large numbers for sequences of pairwise negative quadrant dependent random variables" 1 (1): 281-305, 2006

15 A. Rosalsky, "On the strong law of large numbers for sequences of blockwise independent and blockwise p-orthogonal random elements in Rademacher type p Banach spaces" 27 (27): 205-222, 2007

16 S. Csorgo, "On the strong law of large numbers for pairwise independent random variables" 42 (42): 319-330, 1983

17 V. F. Gaposhkin, "On the strong law of large numbers for blockwise independent and blockwise orthogonal random variables" 39 : 667-684, 1995

18 L. V. Thanh, "On the Brunk-Chung type strong law of large numbers for sequences of blockwise m-dependent random variables" 10 : 258-268, 2006

19 T. C. Hu, "On pairwise independent and independent exchangeable random variables" 15 (15): 51-57, 1997

20 B. D. Choi, "On convergence of (Sn-ESn)=n1=r, 1 < r < 2, for pairwise independent random variables" 22 (22): 79-82, 1985

21 E. B. Czerebak-Mrozowicz, "Marcinkiewicz-type strong law of large numbers for pairwise independent random fields" 22 (22): 127-139, 2002

22 D. H. Hong, "Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables" 22 (22): 171-177, 1999

23 V. M. Kruglov, "Growth of sums of pairwise independent random variables with infinite means" 51 (51): 359-362, 2007

24 D. Wei, "Convergence of weighted sums of tight random elements" 8 (8): 282-294, 1978

25 T. K. Chandra, "Cesaro uniform integrability and the strong law of large numbers" 54 : 215-231, 1992

26 A. Bose, "Cesaro uniform integrability and Lp convergence" 55 : 12-28, 1993

27 N, Etemadi, "An elementary proof of the strong law of large numbers" 55 (55): 119-122, 1981

28 V. M. Kruglov, "A strong law of large numbers for pairwise independent identically distributed randV. M. Kruglovom variables with infinite means" 78 (78): 890-895, 2008