Large Deviations for Sums of Independent Non Identically Distributed Random Variables

Abstract

Abstract This article considers large deviation results for sums of independent non identically distributed random variables, generalizing the result of Petrov (1968 Petrov , V. V. ( 1968 ). Asymptotic behavior of probabilities of large deviations . Theor. Probab. Appl. 13 : 408 – 420 .[Crossref] , [Google Scholar]) by using a weaker and more natural condition on bounds of the cumulant generating functions of the sequence of random variables. Keywords: Asymptotic expansionsCramér's conditionLarge deviationLimit theoremsSums of independent random variablesMathematics Subject Classification: 60F1060G5062E20 Acknowledgment This research was supported by ARC Discovery Grant DP0451722 and RFFI grant 07-01-00688.