A note on sums of independent random variables
نویسندگان
چکیده
منابع مشابه
A Note on Sums of Independent Random Variables
provided (Xn) are either symmetric or positive, and in the first case p ≥ 2, and in the second case p ≥ 1. The main novelty here is the fact that, contrary to the classical inequalities, the constants here are independent of p. Certain particular cases of Lata la’s result had been known earlier (see e.g. Hitczenko (1993), Gluskin and Kwapień (1995) or Hitczenko, Montgomery-Smith and Oleszkiewic...
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In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lataa la on bounds on moments of such sums. We also give a new proof of Lataa la's result for nonnegative random variables, and improve one of the constants in his inequality.
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The paper deals with a problem proposed by Uriel Feige in 2005: if X1, . . . , Xn is a set of independent nonnegative random variables with expectations equal to 1, is it true that P ( ∑n i=1 Xi < n + 1) > 1 e ? He proved that P ( ∑n i=1Xi < n + 1) > 1 13 . In this paper we prove that infimum of the P ( ∑n i=1Xi < n + 1) can be achieved when all random variables have only two possible values, a...
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2 . The invariance principle . We first prove the following : If the theorem can be established for one particular sequence of independent random variables Y1, Y2, . . . satisfying the conditions of the theorem then the conclusion of the theorem holds for all sequences of independent random variables which satisfy the conditions of the theorem . In other words, if the limiting distribution exis...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1961
ISSN: 0386-5991
DOI: 10.2996/kmj/1138844471