Comparisons between tail probabilities of sums of independent symmetric random variables
Pruss, Alexander R.
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997), p. 651-671 / Harvested from Numdam
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Publié le : 1997-01-01
@article{AIHPB_1997__33_5_651_0,
     author = {Pruss, Alexander R.},
     title = {Comparisons between tail probabilities of sums of independent symmetric random variables},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {33},
     year = {1997},
     pages = {651-671},
     mrnumber = {1473569},
     zbl = {0893.60009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1997__33_5_651_0}
}

Pruss, Alexander R. Comparisons between tail probabilities of sums of independent symmetric random variables. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) pp. 651-671. http://gdmltest.u-ga.fr/item/AIHPB_1997__33_5_651_0/

[1] A. Bikelis [= BIKYALIS], On estimates of the remainder term in the central limit theorem, Litovskiĭ Mat. Sb., Vol. 6, 1966, p. 323-346 (Russian). | MR 210173 | Zbl 0149.14002

[2] D.L. Burkholder, Explorations in martingale theory and its applications, Ecole d'Eté de Probabilités de Saint-Flour XIX - 1989 (D. L. Burkholder, E. Padoux and A. Sznitman, eds.), Lecture Notes in Mathematics, Vol. 1464, Springer-Verlag, New York, 1991, p. 1-66. | MR 1108183 | Zbl 0771.60033

[3] R. Chen, A remark on the tail probability of a distribution, J. Multivariate Analysis, Vol. 8, 1978, p. 328-333. | MR 482945 | Zbl 0376.60033

[4] P. Erdös, On a theorem of Hsu and Robbins, Ann. Math. Statist., Vol. 20, 1949, p. 286-291. | MR 30714 | Zbl 0033.29001

[5] P. Erdös, Remark on my paper "On a theorem of Hsu and Robbins", Ann. Math. Statist., Vol. 21, 1950, p. 138. | MR 32970 | Zbl 0035.21403

[6] B.V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, revised, Addison-Wesley, Reading, Massachusetts, 1968. | MR 233400

[7] A. Gut, Complete convergence, Asymptotic Statistics: Proceedings of the Fifth Symposium held at Charles University, Prague, September 4-9, 1993 (P. Mandl and M. Hušková, eds.), Contrib. Statist., Physica-Verlag, Heidelberg. | MR 1311943

[8] A. Gut, Complete convergence for arrays, Periodica Math. Hungarica, Vol. 25, 1992, p. 51-75. | MR 1200841 | Zbl 0760.60029

[9] C.C. Heyde, A supplement to the strong law of large numbers, J. Appl. Prob., Vol. 12, 1975, p. 173-175. | MR 368116 | Zbl 0305.60008

[10] P.L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A., Vol. 33, 1947, p. 25-31. | MR 19852 | Zbl 0030.20101

[11] C.S. Kahane, Evaluating Lebesgue integrals as limits of Riemann sums, Math. Japonica, Vol. 38, 1993, p. 1073-1076. | MR 1250330 | Zbl 0795.28004

[12] O.I. Klesov, Convergence of series of probabilities of large deviations of sums of independent identically distributed random variables, Ukraïnskiĭ Mat. Zhurn., Vol. 45, 1993, p. 770-784. | MR 1299963 | Zbl 0805.60021

[13] S. Kwapień and W.A. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Birkhauser, Boston, 1992. | MR 1167198 | Zbl 0751.60035

[14] D. Li, M.B. Rao, T. Jiang and X. Wang, Convergence and almost sure convergence of weighted sums of random variables, J. Theoret. Probab., Vol. 8, 1995, p. 49-76. | MR 1308670 | Zbl 0814.60026

[15] M. Loève, Probability Theory, 3rd edition, Van Nostrand, New York, 1963. | MR 203748 | Zbl 0108.14202

[16] S.J. Montgomery-Smith, Comparison of sums of identically distributed random vectors, Probab. Math. Statist., Vol. 14, 1993, p. 281-285. | MR 1321767 | Zbl 0827.60005

[17] A.R. Pruss, On Spătaru's extension of the Hsu-Robbins-Erdös law of large numbers, J. Math. Anal. Appl., Vol. 199, 1996, p. 558-578. | MR 1383241 | Zbl 0853.60042

[18] A.R. Pruss, Randomly sampled Riemann sums and complete convergence in the law of large numbers for a case without identical distribution, Proc. Amer. Math. Soc., Vol. 124, 1996, p. 919-929. | MR 1301524 | Zbl 0843.60031

[19] A.R. Pruss, A two-sided estimate in the Hsu-Robbins-Erdös law of large numbers, Stochastic Processes Appl. (to appear). | MR 1475661 | Zbl 0911.60021

[20] A.R. Pruss, Remarks on summability of series formed from deviation probabilities of sums of independent identically distributed random variables, Ukraïnskiĭ Mat. Zhurn., Vol. 48, 1996, p. 569-572. | MR 1417021 | Zbl 0946.60021

[21] A.R. Pruss, A bounded N-tuplewise independent and identically distributed counterexample to the CLT, Preprint, 1997.

[22] D. Szynal, On complete convergence for some classes of dependent random variables, Annales Univ. Mariae Curie-Sklodowska, (Sectio A), Vol. 47, 1993, p. 145-150. | MR 1344984 | Zbl 0876.60016

[23] H. Thorisson, Coupling methods in probability theory, Scand. J. Statist., Vol. 22, 1995, p. 159-182. | MR 1339749 | Zbl 0839.60070

[24] W.A. Woyczyński, Tail probabilities of sums of random vectors in Banach spaces, and related norms, Measure Theory Oberwolfach 1979 (D. Kolzow, ed.), Lecture Notes in Mathematics, Vol. 794, Springer-Verlag, New York, 1980, p. 455-469. | MR 577990 | Zbl 0436.60007

[25] W.A. Woyczyński, On Marcinkiewicz-Zygmund laws of large numbers in Banach spaces and related rates of convergence, Probab. Math. Statist., Vol. 1, 1980, p. 117-131. | MR 626306 | Zbl 0502.60006