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Some local limit results in fluctuation theory

Published online by Cambridge University Press:  09 April 2009

C. C. Heyde
C. C. Heyde
Affiliation:
The University of SheffieldEngland
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Let Xi, ι = 1, 2, 3,… be a sequence of independent and identically distributed random variables and write S0 = 0, Sn = ∑ni=1Xi, n ≧ 1. Nn is the number of positive terms in the sequence S0, S1, S2,…, Snn ≧ 0.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 4 , November 1967 , pp. 455 - 464
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Baum, L. E. and Katz, M. L., ‘On the influence of moments on the asymptotic distribution of sums of random variables. Ann. Math. Statist. 34 (1963), 1042–1044.CrossRefGoogle Scholar
[2]Feller, W., An introduction to probability theory and its applications, Volume II (Wiley New York 1966).Google Scholar
[3]Heyde, C. C., ‘Some results on small deviation probability convergence rates for sums of independent random variables’, Can. J. Math. 18 (1966), 656–665.CrossRefGoogle Scholar
[4]Rosén, B., ‘On the asymptotic distribution of sums of independent identically distributed random variables’, Arkiv För Matematik 4 (1962), 323–332.CrossRefGoogle Scholar
[5]Andersen, E. Sparre, ‘On sums of symmetrically dependent random variables’, Skand. Aktuar. 36 (1953), 123–138.Google Scholar
[6]Andersen, E. Sparre, ‘On the fluctuations of sums of independent random variables II’, Math. Scand. 2 (1954), 195–223.Google Scholar
[7]Spitzer, F. L., ‘A combinatorial lemma and its application to probability theory’, Trans. Amer. Math. Soc. 82 (1956), 323–339.CrossRefGoogle Scholar
[8]Spitzer, F. L., Principles of Random Walk (Van Nostrand, New York 1964).CrossRefGoogle Scholar