Abstract
We obtain precise large deviations for heavy-tailed random sums \(S(t) = \sum\nolimits_{i = 1}^{N(t)} {X_i ,t \geqslant 0} \), of independent random variables. \((N(t))_{t \geqslant 0} \) are nonnegative integer-valued random variables independent of r.v. (X i )i \( \in \)N with distribution functions F i. We assume that the average of right tails of distribution functions F i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given.
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Skučaitė, A. Large Deviations for Sums of Independent Heavy-Tailed Random Variables. Lithuanian Mathematical Journal 44, 198–208 (2004). https://doi.org/10.1023/B:LIMA.0000033784.64716.74
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DOI: https://doi.org/10.1023/B:LIMA.0000033784.64716.74