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

Abstract

We prove large deviation results on the partial and random sums s n =Σ i=1 n X i , n⩾1; S(t)=Σ i=1 N(t) X i , t⩾0, where {N(t);t⩾0} are non-negative integer-valued random variables and {X n ;n⩾1} are independent non-negative random variables with distribution, F n , of X n , independent of {N(t);t⩾0}. Special attention is paid to the distribution of dominated variation.