Abstract
We prove large deviation results on the partial and random sums s n =Σ n i=1 X i , n⩾1; S(t)=Σ N(t) i=1 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.
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Liu, Y., Hu, Y. Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails. Sci. China Ser. A-Math. 46, 383–395 (2003). https://doi.org/10.1360/03ys9041
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DOI: https://doi.org/10.1360/03ys9041