Note on successive cumulative 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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as iV—> 00. In the particular case when JUJV = 0 and a = 6, the limit values of (1.2) and (1.3) were recently obtained by Erdös and Kac [ l ] . 1 The case when [INT^O, especially when /i^iV converges to a finite value, is of particular importance in the theory of sequential tests of statistical hypotheses. I t will be seen in §3 that the limit distribution of the number of observations required...
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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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We investigate the asymptotic behavior of the uniform distance between the distributions of the random maximum of cumulative sums and suPte[o. l]WU where Wt is the Wiener process. It is assumed here that the variates are independent and identically distributed. We show that, under some weak conditions on the random index of the maximum, the approximation order of the uniform distance is as shar...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1949
ISSN: 1802-114X
DOI: 10.21136/cpmf.1949.109148