Science in China Series A: Mathematics

, Volume 46, Issue 3, pp 383–395 | Cite as

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

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Abstract

We prove large deviation results on the partial and random sums s n 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.

Keywords

large deviations (extended) regular variation dominated variation 

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© Science in China Press 2003

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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