On the weak law of large numbers for normed weighted sums of i.i.d. random variables.
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Adler, André, Rosalsky, Andrew (1991)
International Journal of Mathematics and Mathematical Sciences
Denisov, D. Eh., Foss, S. G. (2003)
Sibirskij Matematicheskij Zhurnal
Rafał Latała (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular then weak tail domination implies strong tail domination. In particular, a positive answer to Oleszkiewicz's question would follow from the so-called Bernoulli conjecture. We also prove that any unconditional logarithmically concave distribution is strongly dominated by a product symmetric exponential measure.
Alexander R. Pruss (1997)
Annales de l'I.H.P. Probabilités et statistiques
Eichelsbacher, Peter, König, Wolfgang (2008)
Electronic Journal of Probability [electronic only]
Shaul R. Foguel, Nassif A. Ghoussoub (1979)
Annales de l'I.H.P. Probabilités et statistiques
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