Summary
We derive necessary and sufficient conditions for several characterizations of the rate of convergence of a sum of independent variables to a stable law. The technique used is to obtain upper and lower bounds on the rate in terms of functions depending in a very simple way on the common underlying distribution. This permits a general approach to the problem of rates of convergence.
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Hall, P. Two-sided bounds on the rate of convergence to a stable law. Z. Wahrscheinlichkeitstheorie verw Gebiete 57, 349–364 (1981). https://doi.org/10.1007/BF00534829
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DOI: https://doi.org/10.1007/BF00534829