The convergence rate for the strong law of large numbers: General lattice distributions |
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| Authors: | James Allen Fill Michael J Wichura |
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| Institution: | 1. Department of Mathematical Sciences, The John Hopkins University, 220 Maryland Hall, 34th and Charles Streets, 21218, Baltimore, MD, USA
2. Department of Statistics, The University of Chicago, 5734 S. University Avenue, 60637, Chicago, IL, USA
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| Abstract: | LetX
1,X
2, ... be a sequence of independent random variables with common lattice distribution functionF having zero mean, and let (S
n
) be the random walk of partial sums. The strong law of large numbers (SLLN) implies that for any    and  >0
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