Abstract
We shall consider a sequence of independent random variables {X n } having a common distribution with finite positive variance σ2 and a mean value which we can take to be zero, without loss of generality. We shall write \({S_n} = \sum\limits_{j = 1}^n {{X_j}} , {F_n}\left( x \right) = P\left( {\frac{{{s_n}}}{{\sigma \sqrt n }} < x} \right)\) . We have F n (x) → Φ(x) uniformly in x. Therefore when x = O(1) we have
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© 1975 Springer-Verlag Berlin · Heidelberg
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Petrov, V.V. (1975). Probabilities of Large Deviations. In: Sums of Independent Random Variables. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65809-9_8
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DOI: https://doi.org/10.1007/978-3-642-65809-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65811-2
Online ISBN: 978-3-642-65809-9
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