A theorem about the oscillation of sums of independent random variables
Authors:
D. L. Hanson and F. T. Wright
Journal:
Proc. Amer. Math. Soc. 37 (1973), 226233
MSC:
Primary 60G50; Secondary 60J15
MathSciNet review:
0315779
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Abstract: Let be i.i.d. random variables and let . The relationship between the tth moment of and the convergence of the series is investigated in this paper. The convergence of the series above when but is related to the oscillation of the sequence and to the oscillation of the sequence about zero.
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 [1]
 D. L. Hanson and Melvin Katz, On the oscillation of sums of random variables, Proc. Amer. Math. Soc. 17 (1966), 864865. MR 33 #3325. MR 0195122 (33:3325)
 [2]
 C. C. Heyde, Two probability theorems and their application to some first passage problems, J. Austral. Math. Soc. 4 (1964), 214222. MR 32 #486. MR 0183004 (32:486)
 [3]
 Einar Hille, Analytic function theory. Vol. 1. Introduction to higher mathematics, Ginn, Boston, Mass., 1959. MR 21 #6415. MR 0107692 (21:6415)
 [4]
 M. Rosenblatt, On the oscillation of sums of random variables, Trans. Amer. Math. Soc. 72 (1952), 165178. MR 13, 567. MR 0045326 (13:567a)
 [5]
 W. L. Smith, A theorem on functions of characteristic functions and its application to some renewal theoretic random walk problems, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), vol. II: Contributions to Probability Theory, part 2, Univ. of California Press, Berkeley, Calif., 1967, pp. 265309. MR 35 #7373. MR 0216542 (35:7373)
 [6]
 Frank Spitzer, A combinatorial lemma and its application to probability theory, Trans. Amer. Math. Soc. 82 (1956), 323339. MR 18, 156. MR 0079851 (18:156e)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197303157790
PII:
S 00029939(1973)03157790
Keywords:
Oscillation,
oscillation about zero
Article copyright:
© Copyright 1973
American Mathematical Society
