Strong laws of large numbers for weighted sums of ρ ¯ -mixing random variables

Guang-hui Cai

Mathematica Slovaca (2007)

  • Volume: 57, Issue: 4, page [381]-388
  • ISSN: 0139-9918

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Cai, Guang-hui. "Strong laws of large numbers for weighted sums of $\overline{\rho }$-mixing random variables." Mathematica Slovaca 57.4 (2007): [381]-388. <http://eudml.org/doc/34656>.

@article{Cai2007,
author = {Cai, Guang-hui},
journal = {Mathematica Slovaca},
keywords = {strong law of large numbers; weighted sum; -mixing},
language = {eng},
number = {4},
pages = {[381]-388},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Strong laws of large numbers for weighted sums of $\overline\{\rho \}$-mixing random variables},
url = {http://eudml.org/doc/34656},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Cai, Guang-hui
TI - Strong laws of large numbers for weighted sums of $\overline{\rho }$-mixing random variables
JO - Mathematica Slovaca
PY - 2007
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 57
IS - 4
SP - [381]
EP - 388
LA - eng
KW - strong law of large numbers; weighted sum; -mixing
UR - http://eudml.org/doc/34656
ER -

References

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  1. BAI Z. D.-CHENG P. E., Marcinkiewicz strong laws for linear statistics, Statist. Probab. Lett. 46 (2000), 105-112. Zbl0960.60026MR1748864
  2. BAXTER J.-JONES R.-LIN M.-OLSEN J., SLLN for weighted independent indentically distributed random variables, J. Theoret. Probab. 17 (2004), 165-181. MR2054584
  3. BRYC W.-SMOLENSKI W., Moment conditions for almost sure convergence of weakly correlated random variables, Proc. Amer. Math. Soc. 2 (1993), 629-635. (1993) Zbl0785.60018MR1149969
  4. CHOI B. D.-SUNG S. H., Almost sure convergence theorems of weighted sums of random variables, Stochastic Anal. Appl. 5 (1987), 365-377. (1987) Zbl0633.60049MR0912863
  5. CHOW Y. S.-TEICHER H., Probability Theory: Independence, Inter changeability, Martingales, (3rd ed.), Springer-Verlag, New York, 1997. (1997) MR1476912
  6. CUZICK J., A strong law for weighted sums of i.i.d. random variables, J. Theoret. Probab. 8 (1995), 625-641. (1995) Zbl0833.60031MR1340830
  7. ERDÖS P., On a theorem of Hsu-Robbins, Ann. Math. Statist. 20 (1949), 286-291. (1949) MR0030714
  8. HSU P. L.-ROBBINS H., Complete convergence and the law of larege numbers, Proc. Nat. Acad. Sci. (USA) 33 (1947), 25-31. (1947) MR0019852
  9. JOAG D. K.-PROSCHAN F., Negative associated of random variables with application, Ann. Statist. 11 (1983), 286-295. (1983) MR0684886
  10. PELIGRAD M., On the asymptotic normality of sequences of weak dependent random variables, J. Theoret. Probab. 9 (1996), 703-715. (1996) Zbl0855.60021MR1400595
  11. PELIGRAD M., Maximum of partial sums and an invariance principle for a class weak depend random variables, Proc. Amer. Math. Soc. 126 (1998), 1181-1189. (1998) MR1425136
  12. PELIGRAD M.-GUT A., Almost sure results for a class of dependent random variables, J. Theoret. Probab. 12 (1999), 87-104. (1999) Zbl0928.60025MR1674972
  13. PETROV V. V., Limit Theorems of Probability Theory Sequences of Independent Random Variables, Oxford Science Publications, Oxford, 1995. (1995) Zbl0826.60001MR1353441
  14. SHAO Q. M., A comparison theorem on moment inequalities between Negatively associated and independent random variables, J. Theoret. Probab. 13 (2000), 343-356. Zbl0971.60015MR1777538
  15. STOUT W., Almost Sure Convergence, Academic Press, New York, 1974. (1974) Zbl0321.60022MR0455094
  16. SUNG S. H., Strong laws for weighted sums of i.i.d. random variables, Statist. Probab. Lett. 52 (2001), 413-419. Zbl1027.60028MR1841609
  17. UTEV S.-PELIGRAD M., Maximal inequalities and an invariance principle for a class of weakly dependent random variables, J. Theoret. Probab. 16 (2003), 101-115. Zbl1012.60022MR1956823
  18. WU W. B., On the strong convergence of a weighted sums, Statist. Probab. Lett 44 (1999), 19-22. (1999) 

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