Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails

Let {X-k, k >= 1} be a sequence of negatively dependent random variables with common distribution F and mean 0. Suppose that (F) over bar (x) = 1 - F(x) is positive for all x and consistently varying as x -> infinity. Let {theta(k), k >= 1} be another sequence of random variables independent of {X-k, k >= 1} satisfying P(a <= theta(k) <= b) = 1 for some 0 < a <= b < infinity, k >= 1. The paper investigates large deviations for the randomly weighted sums. (C) 2008 Elsevier B.V. All rights reserved.