Some more results on rates of convergence in the law of large numbers for weighted sums of independent random variables
HTML articles powered by AMS MathViewer
- by D. L. Hanson and F. T. Wright PDF
- Trans. Amer. Math. Soc. 141 (1969), 443-464 Request permission
References
- Leonard E. Baum and Melvin Katz, Convergence rates in the law of large numbers, Bull. Amer. Math. Soc. 69 (1963), 771–772. MR 156373, DOI 10.1090/S0002-9904-1963-11027-7 —, Convergence rates in the law of large numbers. II, Tech. Rep. No. 75, Dept. of Math. and Stat., Univ. of New Mexico, Albuquerque, 1964.
- Y. S. Chow, Some convergence theorems for independent random variables, Ann. Math. Statist. 37 (1966), 1482–1493. MR 203779, DOI 10.1214/aoms/1177699140
- James Avery Davis, Convergence rates for the law of the iterated logarithm, Ann. Math. Statist. 39 (1968), 1479–1485. MR 253411, DOI 10.1214/aoms/1177698029
- James Avery Davis, Convergence rates for probabilities of moderate deviations, Ann. Math. Statist. 39 (1968), 2016–2028. MR 235599, DOI 10.1214/aoms/1177698029
- W. E. Franck and D. L. Hanson, Some results giving rates of convergence in the law of large numbers for weighted sums of independent random variables, Trans. Amer. Math. Soc. 124 (1966), 347–359. MR 199877, DOI 10.1090/S0002-9947-1966-0199877-1
- D. L. Hanson, Some results relating moment generating functions and convergence rates in the law of large numbers, Ann. Math. Statist. 38 (1967), 742–750. MR 215342, DOI 10.1214/aoms/1177698867
- D. L. Hanson and L. H. Koopmans, A probability bound for integrals with respect to stochastic processes with independent increments, Proc. Amer. Math. Soc. 16 (1965), 1173–1177. MR 184281, DOI 10.1090/S0002-9939-1965-0184281-7
- C. C. Heyde, On almost sure convergence for sums of independent random variables, Sankhyā Ser. A 30 (1968), 353–358. MR 279865 V. K. Rohatgi, On convergence rates in the law of large numbers for weighted sums of independent random variables, Res. Rep. No. 26, Dept. of Prob. and Stat., Univ. of Sheffield, 1967.
- William F. Stout, Some results on the complete and almost sure convergence of linear combinations of independent random variables and martingale differences, Ann. Math. Statist. 39 (1968), 1549–1562. MR 232429, DOI 10.1214/aoms/1177698136
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 141 (1969), 443-464
- MSC: Primary 60.30
- DOI: https://doi.org/10.1090/S0002-9947-1969-0247650-0
- MathSciNet review: 0247650