On large deviations for sums of independent random variables

Valentin V. Petrov, John Robinson

Abstract

This paper considers large deviation results for sums of independent random variables, generalizing the result of Petrov (1968) by using a weaker and more natural condition on bounds of the cumulant generating functions of the sequence of random variables.

Keywords Limit theorems, sums of independent random variables, large deviation, Cramér's condition, asymptotic expansions.

AMS Subject Classification Primary 60F10; secondary 60G50, 62E20.