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Lithuanian Mathematical Journal

, Volume 45, Issue 4, pp 359–367 | Cite as

On Cramer Approximations under Violation of Cramer's Condition

  • A. K. Aleskeviciene
Article
  • 33 Downloads

Abstract

Let X1, X2,... be independent identically distributed random variables with distribution function F, S0 = 0, S n = X1 + ⋯ + X n , and n = max1⩽knS k . We obtain large-deviation theorems for S n and n under the condition 1 − F(x) = P{X1x} = el(x), l(x) = xαL(x), α ∈ (0, 1), where L(x) is a slowly varying function as x → ∞.

Keywords

sums of random variables maxima of sums large deviations 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. K. Aleskeviciene
    • 1
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania

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