Tail and moment estimates for sums of independent random vectors with logarithmically concave tails

• Autorzy: Rafał Latała
• Języki publikacji: EN

Abstrakty

EN

Let $X_i$ be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable $X = ∑v_{i}X_{i}$, where $v_i$ are vectors of some Banach space. We derive approximate formulas for the tail and moments of ∥X∥. The estimates are exact up to some universal constant and they extend results of S. J. Dilworth and S. J. Montgomery-Smith [1] for the Rademacher sequence and E. D. Gluskin and S. Kwapień [2] for real coefficients.

Kategorie tematyczne

• 60G50: Sums of independent random variables; random walks
• 60B11: Probability theory on linear topological spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 118
• Numer: 3
• Strony: 301-304

Daty

wydano

1996

otrzymano

1995-11-07

Twórcy

autor

Rafał Latała

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

Bibliografia

• [1] S. J. Dilworth and S. J. Montgomery-Smith, The distribution of vector-valued Rademacher series, Ann. Probab. 21 (1993), 2046-2052.
• [2] E. D. Gluskin and S. Kwapień, Tail and moment estimates for sums of independent random variables with logarithmically concave tails, Studia Math. 114 (1995), 303-309.
• [3] P. Hitczenko and S. Kwapień, On the Rademacher series, in: Probability in Banach Spaces 9, Birkhäuser, Boston, 31-36.
• [4] B. Maurey, Some deviation inequalities, Geom. Funct. Anal. 1 (1991), 188-197.
• [5] M. Talagrand, A new isoperimetric inequality and the concentration of measure phenomenon, in: Israel Seminar (GAFA), Lecture Notes in Math. 1469, Springer, 1991, 94-124.