Abstract: | In this paper we consider the large deviations for random sums
, 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. |