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Large deviation theorems for weighted compound Poisson sums

Bonin O.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 2

357--368

In this paper we present two large deviation results for weighted compound sums ∑Ni = 1 ai Xi, where Xi’s are i.i.d. (possibly lattice) random variables, ai’s are non-negative real numbers, and N is a Poisson variable. These results are generalizations of approximations for non-weighted compound sums and for non-compound weighted sums.