Abstract
In this paper we consider the large deviations for random sums\(S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0\), whereX n,n⩾1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t⩾0 is a process of non-negative integer-valued random variables, independent ofX n,n⩾1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t⩾0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.
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Su, C., Tang, Q. & Jiang, T. A contribution to large deviations for heavy-tailed random sums. Sci. China Ser. A-Math. 44, 438–444 (2001). https://doi.org/10.1007/BF02881880
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DOI: https://doi.org/10.1007/BF02881880