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- W2062790704 abstract "Let the random variables $$X_i, i = 1, 2, 3, ldots$$ be independent and identically distributed. Write $$S_n = sum^{n}_{i=1} X_i , {rm and}, Z_n = S_n B^{-1}_n - A_n$$ for normed and centered sums. The classical central limit formulation is for $${rm Pr} (Z_n leqq x_n)$$ where x n = 0(1) as $$n rightarrow infty$$ and thus gives only trivial information in the case where $$x_n rightarrow infty$$ as $$n rightarrow infty$$ . However, we often require information on $${rm Pr} (Z_n > x_n)$$ under these circumstances. This type of problem is called a problem on the probability of large deviations and little in the way of comprehensive general results on such problems has so far been obtained. For references to the known results and also to various fields in which large deviation problems arise see, for example, Linnik [3] and Sethuraman [7]." @default.
- W2062790704 created "2016-06-24" @default.
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- W2062790704 date "2010-01-01" @default.
- W2062790704 modified "2023-10-09" @default.
- W2062790704 title "A Contribution to the Theory of Large Deviations for Sums of Independent Random Variables" @default.
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