On Weak Tail Domination of Random Vectors
Tom 57 / 2009
Bulletin Polish Acad. Sci. Math. 57 (2009), 75-80
MSC: Primary 60E15; Secondary 60G50, 52A40.
DOI: 10.4064/ba57-1-8
Streszczenie
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.
