Precise asymptotics in Spitzer and Baum-Katz's law of large numbers: the semistable case |
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Authors: | Hans-Peter Scheffler |
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Affiliation: | Fachbereich Mathematik, University of Dortmund, 44221 Dortmund, Germany |
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Abstract: | Let X1,X2,… be i.i.d. random variables with distribution μ and with mean zero, whenever the mean exists. Set Sn=X1+?+Xn. In recent years precise asymptotics as ε↓0 have been proved for sums like ∑n=1∞n−1P{|Sn|?εn1/p}, assuming that μ belongs to the (normal) domain of attraction of a stable law. Our main results generalize these results to distributions μ belonging to the (normal) domain of semistable attraction of a semistable law. Furthermore, a limiting case new even in the stable situation is presented. |
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Keywords: | Tail probabilities of sums of i.i.d. random variables Semistable distributions Spitzer's law Baum-Katz's law |
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