Large deviations for sums of independent random variables with dominatedly varying tails

In this paper the large deviation results for partial and random sums are proved, where {N(t); t ≥ 0} is a counting process of non-negative integer-valued random variables, and {X _n ; n ≥ 1} are a sequence of independent non-negative random variables independent of {N(t); t ≥ 0}. These results extend and improve some known conclusions. Supported by the Science Foundation of the Education Committee of Anhui Province(0505101).