Displaying similar documents to “On the functional equation f ( x + y ) f ( x - y ) = f 2 ( x ) - f 2 ( y ) ”

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

Rafał Latała (1996)

Studia Mathematica

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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.