Some more results on rates of convergence in the law of large numbers for weighted sums of independent random variables

Authors:
D. L. Hanson and F. T. Wright

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

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References | Similar Articles | Additional Information

**[1]**L. E. Baum and Melvin Katz,*Convergence rates in the law of large numbers*, Bull. Amer. Math. Soc.**69**(1963), 771-772. MR**0156373 (27:6296)****[2]**-,*Convergence rates in the law of large numbers*. II, Tech. Rep. No. 75, Dept. of Math. and Stat., Univ. of New Mexico, Albuquerque, 1964.**[3]**Y. S. Chow,*Some convergence theorems for independent random variables*, Ann. Math. Statist.**37**(1966), 1482-1493. MR**0203779 (34:3627)****[4]**James Avery Davis,*Convergence rates for the law of the iterated logarithm*. Ann. Math. Statist.**39**(1968), 1479-1485. MR**0253411 (40:6626)****[5]**-,*Convergence rates for probabilities of moderate deviations*, Ann. Math. Statist.**39**(1968), 2016-2028. MR**0235599 (38:3903)****[6]**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**0199877 (33:8017)****[7]**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**0215342 (35:6183)****[8]**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**0184281 (32:1754)****[9]**C. C. Heyde,*On almost sure convergence for sums of independent random variables*, Res. Rep. No. 27, Dept. of Prob. and Stat., Univ. of Sheffield, 1967. MR**0279865 (43:5586)****[10]**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.**[11]**William 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**0232429 (38:754)**

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DOI:
https://doi.org/10.1090/S0002-9947-1969-0247650-0

Article copyright:
© Copyright 1969
American Mathematical Society