Maximal inequalities for centered norms of sums of independent random vectors
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چکیده
Let X1, X2, . . . , Xn be independent random variables and Sk = Pk i=1 Xi. We show that for any constants ak, P( max 1≤k≤n ||Sk| − ak| > 11t) ≤ 30 max 1≤k≤n P(||Sk| − ak| > t). We also discuss similar inequalities for sums of Hilbert and Banach space valued random vectors.
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