On weak tail domination of random vectors

• Autorzy: Latała R.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

sums of independent random variables; Bernoulli series; random vectors; log-concave distributions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 1
• Strony: 75--80
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Latała R.

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland,

Bibliografia

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• [5] S. Kwapień and W. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston, 1992.
• [6] R. Latała, Sudakov minoration principle and supremum of some processes, Geom. Funct. Anal. 7 (1997), 936-953.
• [7] M. Talagrand, Regularity of Gaussian processes, Acta Math. 159 (1987), 99-149.
• [8] M. Talagrand, The supremum of some canonical processes, Amer. J. Math. 116 (1994), 284-325.
• [9] M. Talagrand, The Generic Chaining. Upper and Lower Bounds of Stochastic Processes, Springer, Berlin, 2005.