On strong limit theorems concerning delayed sums of a random sequence

被引:0
作者
Zhong-Zhi Wang
机构
[1] AnHui University of Technology,School of Mathematics & Physics
来源
Acta Mathematica Hungarica | 2013年 / 141卷
关键词
limit theorem; delayed sum; information source; 60F15; 94A17;
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摘要
Let (ξn)n∈N be a sequence of arbitrarily dependent random variables. In this paper, a generalized strong limit theorem of the delayed average of (ξn)n∈N is investigated, then some limit theorems for arbitrary information sources follow. As corollaries, some known results are generalized.
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页码:329 / 338
页数:9
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  • [1] Algoet P. H.(1988)A sandwich proof of the Shannon–McMillan–Breiman theorem Ann. Probab. 16 899-909
  • [2] Cover T. M.(1985)Summability methods and almost sure convergence Z. Wahrscheinlichkeitstheorie Verw. Geb. 68 383-392
  • [3] Bingham N. H.(1986)Riesz and Valiron means and fractional moments Math. Proc. Cambridge Philos. Soc. 99 143-149
  • [4] Maejima M.(2008)Limiting behavior of delayed sums under a non-identically distribution setup An. Acad. Bras. Cienc. 80 617-625
  • [5] Bingham N. H.(1973)Delayed sums and Borel summability of independent, identically distributed random variables Bull. Inst. Math., Academia Sinica 1 207-220
  • [6] Tenenbaum G.(1997)A note on the empirical distribution of dependent random variables Statist. Probab. Lett. 34 337-340
  • [7] Chen P. Y.(1974)Limit theorems for delayed sums Ann. Probab. 2 432-440
  • [8] Chow Y. S.(2009)A bivariate law of iterated logarithm for partial sums and delayed sums The Open Statistics and Probability Journal 1 65-70
  • [9] Hanson D. L.(undefined)undefined undefined undefined undefined-undefined
  • [10] Gang L.(undefined)undefined undefined undefined undefined-undefined