Chover-type laws of the iterated logarithm for weighted sums of NA sequences

Guang-hui Cai

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 1, page 27-33
  • ISSN: 0862-7959

Abstract

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To derive a Baum-Katz type result, a Chover-type law of the iterated logarithm is established for weighted sums of negatively associated (NA) and identically distributed random variables with a distribution in the domain of a stable law in this paper.

How to cite

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Cai, Guang-hui. "Chover-type laws of the iterated logarithm for weighted sums of NA sequences." Mathematica Bohemica 132.1 (2007): 27-33. <http://eudml.org/doc/250268>.

@article{Cai2007,
abstract = {To derive a Baum-Katz type result, a Chover-type law of the iterated logarithm is established for weighted sums of negatively associated (NA) and identically distributed random variables with a distribution in the domain of a stable law in this paper.},
author = {Cai, Guang-hui},
journal = {Mathematica Bohemica},
keywords = {negatively associated sequence; laws of the iterated logarithm; weighted sum; stable law; Rosental type maximal inequality; negatively associated sequence; laws of the iterated logarithm; weighted sum; stable law; Rosental type maximal inequality},
language = {eng},
number = {1},
pages = {27-33},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Chover-type laws of the iterated logarithm for weighted sums of NA sequences},
url = {http://eudml.org/doc/250268},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Cai, Guang-hui
TI - Chover-type laws of the iterated logarithm for weighted sums of NA sequences
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 1
SP - 27
EP - 33
AB - To derive a Baum-Katz type result, a Chover-type law of the iterated logarithm is established for weighted sums of negatively associated (NA) and identically distributed random variables with a distribution in the domain of a stable law in this paper.
LA - eng
KW - negatively associated sequence; laws of the iterated logarithm; weighted sum; stable law; Rosental type maximal inequality; negatively associated sequence; laws of the iterated logarithm; weighted sum; stable law; Rosental type maximal inequality
UR - http://eudml.org/doc/250268
ER -

References

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  1. 10.1016/S0167-7152(02)00286-9, Statist. Probab. Lett. 60 (2002), 367–375. (2002) Zbl1014.60010MR1947176DOI10.1016/S0167-7152(02)00286-9
  2. The Chover law of the iterated logarithm for random geometric series of stable distribution, Acta Math. Sin. 46 (2000), 1063–1070. (Chinese) (2000) 
  3. 10.1090/S0002-9939-1966-0189096-2, Proc. Amer. Math. Soc. 17 (1966), 441–443. (1966) MR0189096DOI10.1090/S0002-9939-1966-0189096-2
  4. 10.1214/aos/1176346079, Ann. Statist. 11 (1983), 286–295. (1983) MR0684886DOI10.1214/aos/1176346079
  5. Probability in Banach Spaces, Springer, Berlin, 1991. (1991) MR1102015
  6. Limit Theorems on Mixing Random Variables, Kluwer Academic Publishers and Science Press, Dordrecht-Beijing, 1997. (1997) 
  7. Foundation of Probability Limit Theory, Beijing, Higher Education Press, 1999. (1999) 
  8. 10.1016/j.spl.2003.08.009, Statist. Probab. Lett. 65 (2003), 401–410. (2003) MR2039884DOI10.1016/j.spl.2003.08.009
  9. On the law of the iterated logarithm for the partial sum in the domain of attraction of stable distribution, Chin. Ann. Math., Ser. A 17 (1996), 195–206. (Chinese) (1996) MR1397108
  10. 10.1023/A:1007849609234, J. Theor. Probab. 13 (2000), 343–356. (2000) Zbl0971.60015MR1777538DOI10.1023/A:1007849609234
  11. LIL for delayed sums under a non-indentically distributed setup, Theory Prob. Appl. 37 (1992), 534–562. (1992) MR1214358
  12. Strong laws for sums of B -valued mixing random fields, Chinese Ann. Math. 22A (2001), 205–216. (2001) MR1837525
  13. A modified law of iterated logarithm for stable random variable, Theory Prob. Math. Stat. 49 (1994), 69–76. (1994) MR1445249

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